Graph

Problem 1

Identify the quadrilateral formed by the points $(-5,0),(0,4),(5,0),(0,-4)$ . Options: A. Trapezoid B. Rhombus C. Square D. Rectangle.

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Problem 2

Identify the quadrilateral formed by the points (0,0), (0,4), (8,4), (8,0). Options: A. Square B. Trapezoid C. Rectangle D. Rhombus.

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Problem 3

Sketch the curves $y=x^{2}+x$ and $y=-2 \cdot x^{2}+4$ from $x=0$ to $x=2$ . Find the area between them using integrals.

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Problem 4

Vẽ tia $\mathrm{Ax}$ , chọn $\mathrm{B} \in \mathrm{Ax}$ với $\mathrm{AB}=8 \mathrm{~cm}$ , và $\mathrm{C}$ sao cho $\mathrm{AC}=4 \mathrm{~cm}$ .
a) C có nằm giữa A và B không? Tại sao? b) So sánh $\mathrm{CA}$ và $\mathrm{CB}$ . c) C có phải là trung điểm của $\mathrm{AB}$ không? Tại sao?

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Problem 5

Determine which statement is true for the function $f(x)=a\left(2^{x}\right)$ given the values of $a$ and $f(0)$ or $f(1)$ .

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Problem 6

Graph $g(x)=|x-2|$ and compare it to $f(x)=|x|$ . Describe the domain and range. Select the correct translation and range.

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Problem 7

Graph $g(x)=-\frac{1}{4}|x|$ . Compare to $f(x)=|x|$ and describe domain and range. Choose the correct option.

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Problem 8

מצא את הגרף של הפונקציה $f(x)=\sqrt{3-x}$ .

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Problem 9

Graph the intervals $P=(-\infty, 7)$ , $Q=[-3,4]$ , and $R=(2, \infty)$ . Find $P \cup Q$ , $Q \cap R$ , and $P \cap R'$ .

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Problem 10

What is the initial height of a tennis ball dropped from 17.4 cm after $t$ seconds?

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Problem 11

What is the football's greatest height if it reaches 4.9 meters at time $t=1$ ?

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Problem 12

What is the initial height of a tennis ball dropped from a height of $176.4$ cm at time $t=0$ ?

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Problem 13

Find the coordinates of the minimum point of the graph of $x^{2}-7x+11$ .

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Problem 14

Locate points of rectangle $ABCD$ at $A(2,2), B(2,-1), C(-1,-1), D(-1,2)$ , then find its perimeter and area.

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Problem 15

Find the area of the triangle with vertices $(4,4)$ , $(4,0)$ , and $(0,0)$ by counting whole and half squares. 8 sq. units. Which quadrant is the point $(-3,2)$ in? Second.

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Problem 16

Triunghiul echilateral $ABC$ are perimetrul $27 \mathrm{~cm}$ . Găsește lungimea segmentului $MC$ , unde $AN=6 \mathrm{~cm}$ .

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Problem 17

Identify a function that fits the points $(-2, 8)$ , $(1, 5)$ , $(3, 13)$ , and $(5, 29)$ .

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Problem 18

Graph the inequality $10 > x \geq 1$ on a number line.

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Problem 19

Graph the piecewise function: $f(x) = \begin{cases} 4 & \text{for } x \leq -1 \\ x + 3 & \text{for } -1 < x < 4 \\ 2x - 2 & \text{for } x \geq 4 \end{cases}$

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Problem 20

5. Într-un dreptunghi cu $AB=12 \mathrm{~cm}$ și $BC=4 \mathrm{~cm}$ , calculează aria triunghiului $CEO$ și unghiul $BFC$ .

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Problem 21

Calculate the distance $BC$ in triangle $ABC$ where $AB=1.5 \text{ km}$ , $AC=1.2 \text{ km}$ , and $\angle A=50^\circ$ .

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Problem 22

Find $T(1)$ from the graph, explain its meaning, and determine when the temperature reaches $70^{\circ} \mathrm{F}$ .

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Problem 23

Find two consecutive whole numbers that $\sqrt{78}$ is between and justify your answer.

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Problem 24

Zeichne den Graphen für Anettes Inlinerfahrt: Ampelhalt, steiniger Weg, Auto vorlassen, dann Ankunft.

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Problem 25

Der Bus fährt um 8.05 Uhr ab. a) Zeichne den Graphen. b) Wann ist die Endstation erreicht? c) Wie lang ist die Strecke?

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Problem 26

Graph the function defined by $f(x) = x + 5$ .

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Problem 27

Draw the parabola $y=3(x+3)^{2}+4$ , indicating the vertex and where it intersects the axes.

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Problem 28

Sketch the graphs of these equations and their intercepts:
1. $y=-(x-3)^{2}+4$
2. $y=\frac{1}{2}(x+2)^{2}+2$
3. $y=3(x+3)^{2}+4$
4. $y=-2(x-1)^{2}+2$

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Problem 29

Find the slope between points (0,2) and (8,13). Which describes the temperature change per minute: $3.25^{\circ} \mathrm{C}$ , $5.25^{\circ} \mathrm{C}$ , $1.25^{\circ} \mathrm{C}$ , or $7.25^{\circ} \mathrm{C}$ ?

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Problem 30

Graph Fran's weekly earnings ( $\$ 480$ for 40 hours, $18$ for each hour over) if she works $h$ hours over 40.

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Problem 31

Calculate the distance $BC$ in triangle $ABC$ where $AB=1.5$ km, $AC=1.2$ km, and $\hat{A}=50^\circ$ .

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Problem 32

Graph the line given by the equation $y=x-2$ .

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Problem 33

Can nonadjacent angles share vertex $A$ and arm $A B$ ? If yes, provide an example; if no, explain why.

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Problem 34

A blue whale swims 2.5 miles in 5 minutes. Create a graph of distance vs. time. How far does it swim in 1 minute?

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Problem 35

Help Milynn find the center of the next circle for her inscribed triangle. Consider previous circles, rules, and vertex positions.

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Problem 36

Sketch the graph of the function $y=3.2^{x+1}-1$ .

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Problem 37

Find the slope between points (0,0) and (1,30) on the line. Can you find another pair of points with a different slope?

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Problem 38

A marine biologist studies a dolphin's speed. It swims 55 meters in 5 seconds. Graph the distance over time. How far in 1 second?

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Problem 39

Find the slope of the line for the points (1,10) to (2,20) and for (1,10) to (5,50). What does it represent?

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Problem 40

Graph the line given by the equation $y + 2 = 2(x + 1)$ . Select points on the graph and submit.

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Problem 41

What inequality represents a graph with a dashed line, negative slope, y-intercept -3, and shaded region above the line?

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Problem 42

Find the average goals scored per year: 4.5, 4.04, 4.22. Plot these values on a number line in ascending order.

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Problem 43

Measure Sandy's tree height over the years. Draw a slope triangle and check if it shows constant growth. Is the growth linear?

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Problem 44

Sandy measures her tree's height each year: (0,0), (1,1), (2,2), (3,2.5), (4,2.5). Analyze slope triangles to check growth rate.

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Problem 45

Ethan delivers newspapers. Use points (5,200) and (10,400) to find the slope, draw a triangle, and explain its meaning.

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Problem 46

Graph the function $y=\frac{1}{x+2}+2$ .

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Problem 47

Create a system of equations with infinite solutions by graphing a line parallel to $y=-3x-4$ and provide its equation.

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Problem 48

Sketch the graph of $y=3x^{2}-6x+5$ for $0 \leq x \leq 4$ . Identify turning point, intercepts, and state the range of $y$ .

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Problem 49

Sketch the graph of $f(x)=\frac{3}{x+1}+2$ . Include all 6 axis intersections and asymptotes.

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Problem 50

Graph the opposites of the following numbers on a number line and label each point: 15. -3.25, 16. 0.25, 17. -1.5.

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Problem 51

Rhianna claims different functions can share $x$ -intercepts $(-5,0),(2,0),(6,0)$ , domain $[-5,7]$ , and range $[-4,10]$ . Can you find examples?

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Problem 52

Choose the graph of the function $h(x)=\frac{1}{3} x^{2}$ and its parent function.

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Problem 53

Label the second quadrant and answer: a. Give one point's coordinates in the second quadrant. b. Describe the coordinates for points there.

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Problem 54

Plot the points $(-4,1)$ and $(1,-1.5)$ on the coordinate plane. Click to add or remove points.

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Problem 55

Approximate the average rate of change of infections from 0 to 8 days after April 1, 2020, using $P(8) \approx 5.55$ .

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Problem 56

Find the average rate of change of COVID-19 infections from 0 to 8 days, assuming 0 at day 0. Round to two decimals.

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Problem 57

Approximate the average rate of change of infections from 0 to 8 days after April 1, 2020, using $P(8) - P(0)$ .

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Problem 58

Graph the line $-3y = x - 3$ by plotting at least two points on the axes. Use technology to assist you.

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Problem 59

Plot several terms of the logistic equation $x_{t+1}=c x_{t}(1-x_{t})$ with $x_{0}=0.4$ and $c=3.5$ .

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Problem 60

Dibuja un histograma de los tiempos de pago: $19,15,43,39,35,31,27,22,18,14,42,38,13,13,13,41,41,41,37,37,37,33$ . Usa límites de clase 12.5 y ancho 7.

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Problem 61

Approximate the average rate of change of COVID-19 infections in Minnesota from 0 to 8 days after April 1, 2020.

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Problem 62

Calculate the average rates of change for COVID-19 infections in Minnesota over these intervals using $\frac{\Delta y}{\Delta x}$ :
1. 0 to 8 days: (calculate)
2. 8 to 16 days: 0.59 thousand/day
3. 0 to 16 days: 0.46 thousand/day

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Problem 63

Draw the angle $150^{\circ}$ , find its reference angle, and identify the quadrant of its terminal side.

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Problem 64

Graph the function $y=x^{3}$ .

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Problem 65

Find the average rate of change of the function $f(x)=x^{2}+6x+10$ over the interval $[-2,1]$ .

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Problem 66

Sketch a function with a negative average rate of change on the interval $[0,3]$ .

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Problem 67

Create a bar graph for enrollment data: 2006 (2255), 2007 (2363), 2009 (2577), 2010 (2759), 2011 (2605), 2013 (2535), 2014 (2389).

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Problem 68

Plot the points $\left\{\frac{3}{4}, 0, -\frac{5}{4}, -0.5, 1.5\right\}$ on a number line.

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Problem 69

Graphically analyze if the function $g(x)=x^{3}-x$ is even, odd, or neither.

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Problem 70

Graph the line through the point $(-4,-3)$ with slope $m=4$ .

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Problem 71

Graph the line through the point $(-3,-5)$ with a slope of $m=3$ .

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Problem 72

Graph Jeriel's temperature data starting at $56^{\circ} \mathrm{F}$ , rising and falling over the day, ending at $60^{\circ}$ .

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Problem 73

Graph the piecewise function: $f(x)=\begin{cases} 3, & -\infty<x\leq-1 \\ x-3, & -1<x\leq2 \\ x/2, & 2<x\leq\infty \end{cases}$

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Problem 74

Graph the distance from home after $x$ hours for a trip to a park 20 miles away at $40 \mathrm{mph}$ , 2 hours at the park, then return at $20 \mathrm{mph}$ .

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Problem 75

Make a histogram for Steph Curry's scores: $36,30,37,39,38,15,35,38,25,34$ . Use 5-point intervals from $10-15$ to $35-40$ .

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Problem 76

How do you correctly plot the point $(3,6)$ on a coordinate plane? Choose the right method from options a-d.

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Problem 77

Find $x$ where $f(x)=0$ and where $f(x)>0$ using points: $(-21,-6)$ , $(-18,0)$ , $(-9,9)$ , $(-6,6)$ , $(-3,0)$ , $(0,-3)$ , $(6,-6)$ , $(12,0)$ , $(18,6)$ .

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Problem 78

Given the function $f$ with points $(12,0)$ , $(6,-6)$ , $(0,-3)$ , $(-21,-6)$ , $(-18,0)$ , $(-6,6)$ , $(-9,9)$ , $(-3,0)$ , $(18,6)$ , find:
(e) Where is $f(x)=0$ ?
(f) Where is $f(x)>0$ ?
(g) What is the domain of $f$ ?

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Problem 79

Given points on the function $f$ : $(8,0)$ , $(4,-6)$ , $(0,-3)$ , $(-14,-6)$ , $(-2,0)$ , $(-4,6)$ , $(-12,0)$ , answer:
(d) Is $f(-14)$ positive or negative?
(e) Where is $f(x)=0$ ? (Separate answers with commas.)

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Problem 80

Use the graph of $f$ to find $f(12)$ , $f(0)$ , and determine if $f(4)$ is positive or negative.

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Problem 81

Find the values of $x$ where $f(x)=0$ and $f(x)>0$ given points: $(8,0)$ , $(4,-6)$ , $(0,-3)$ , $(-14,-6)$ , $(-2,0)$ , $(-4,6)$ , $(-6,9)$ , $(-12,0)$ .

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Problem 82

Analyze the function $f$ to find where $f(x)=0$ , $f(x)>0$ , and its domain based on the given points.

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Problem 83

Find the domain, range, and $x$ -intercepts of the function $f$ : Domain: $-14 \leq x \leq 12$ , Range: $-6 \leq y \leq 9$ , $x$ -intercepts: $8, -2, -12$ .

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Problem 84

Find the $x$ -intercepts and $y$ -intercepts of the function $f$ with range $-6 \leq y \leq 9$ . $x$ -intercepts: $x=8,-2,-12$ . $y=$

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Problem 85

Find the $y$ -intercept(s) of the points $(8,0)$ , $(4,-6)$ , $(0,-3)$ , $(-14,-6)$ , $(-2,0)$ , $(-4,6)$ , $(-6,9)$ , $(-12,0)$ . How many times does $y=1$ and $x=5$ intersect the graph?

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Problem 86

Analyze the graph of $f$ to find intersections with $y=1$ , $x=5$ , and solve $f(x)=-6$ . Use given points for help.

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Problem 87

Determine the ratios from the points (2,3), (4,6), (6,9), (8,12). For every \_\_\_ cup(s) of water, \_\_\_ cup(s) of flour. When 8 cups of water, \_\_\_ cups of flour needed.

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Problem 88

Graph Grant and Pedro's stock results for Monday, given that Grant lost \$4. How would you represent this?

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Problem 89

Sketch the line given by the equation $4y = 5x - 4$ .

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Problem 90

Find the inequality for the shaded region to the right of the line $x = -\frac{1}{8}$ . Is the line included?

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Problem 91

Plot the features of the function $f(x)=\frac{x-2}{2x+7}$ : vertical asymptote, horizontal asymptote, $x$ -intercept, $y$ -intercept, and hole.

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Problem 92

Use the nearest neighbor algorithm on the graph with edge weights given. Start and end at vertex A. List the vertices.

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Problem 93

Graph the inequality $\left|\frac{1}{2} x + 2\right| \geq 1$ .

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Problem 94

Sketch the least positive angle $\theta$ from the line $-7x - 3y = 0$ where $x \leq 0$ , and find the six trig functions of $\theta$ .

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Problem 95

What does the point $(3,7.5)$ mean in the graph showing twine usage for bundles of wood? (A) 7.5 feet for 7.5 bundles. (B) 7.5 feet for 3 bundles. (C) 3 feet for 7.5 bundles. (D) 3 feet for 3 bundles.

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Problem 96

Graph the inequality $|4x + 2| < 10$ .

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Problem 97

Solve the inequality $-16 \leq -2x - 6 \leq 0$ and graph the solution.

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Problem 98

Find the intercepts, domain, range, and intervals of increase/decrease for the function $f$ with points (-3,3), (-2,0), (0,1), (2,0), (3,3). Is it even, odd, or neither?

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Problem 99

Reflect the square CDEF with vertices C(3,2), D(10,2), E(10,9), F(3,9) over the line $y=-x$ .

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Problem 100

Construct a figure where $\overline{XY}$ is perpendicular to $\overline{YZ}$ . What are the first and second steps?

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118

Graph

Problem 1

Identify the quadrilateral formed by the points (−5,0),(0,4),(5,0),(0,−4)(-5,0),(0,4),(5,0),(0,-4)(−5,0),(0,4),(5,0),(0,−4). Options: A. Trapezoid B. Rhombus C. Square D. Rectangle.

Problem 2

Identify the quadrilateral formed by the points (0,0), (0,4), (8,4), (8,0). Options: A. Square B. Trapezoid C. Rectangle D. Rhombus.

Problem 3

Sketch the curves y=x2+xy=x^{2}+xy=x2+x and y=−2⋅x2+4y=-2 \cdot x^{2}+4y=−2⋅x2+4 from x=0x=0x=0 to x=2x=2x=2. Find the area between them using integrals.

Problem 4

Problem 5

Determine which statement is true for the function f(x)=a(2x)f(x)=a\left(2^{x}\right)f(x)=a(2x) given the values of aaa and f(0)f(0)f(0) or f(1)f(1)f(1).

Problem 6

Graph g(x)=∣x−2∣g(x)=|x-2|g(x)=∣x−2∣ and compare it to f(x)=∣x∣f(x)=|x|f(x)=∣x∣. Describe the domain and range. Select the correct translation and range.

Problem 7

Graph g(x)=−14∣x∣g(x)=-\frac{1}{4}|x|g(x)=−41​∣x∣. Compare to f(x)=∣x∣f(x)=|x|f(x)=∣x∣ and describe domain and range. Choose the correct option.

Problem 8

מצא את הגרף של הפונקציה f(x)=3−xf(x)=\sqrt{3-x}f(x)=3−x​.

Problem 9

Graph the intervals P=(−∞,7)P=(-\infty, 7)P=(−∞,7), Q=[−3,4]Q=[-3,4]Q=[−3,4], and R=(2,∞)R=(2, \infty)R=(2,∞). Find P∪QP \cup QP∪Q, Q∩RQ \cap RQ∩R, and P∩R′P \cap R'P∩R′.

Problem 10

What is the initial height of a tennis ball dropped from 17.4 cm after ttt seconds?

Problem 11

What is the football's greatest height if it reaches 4.9 meters at time t=1t=1t=1?

Problem 12

What is the initial height of a tennis ball dropped from a height of 176.4176.4176.4 cm at time t=0t=0t=0?

Problem 13

Find the coordinates of the minimum point of the graph of x2−7x+11x^{2}-7x+11x2−7x+11.

Problem 14

Locate points of rectangle ABCDABCDABCD at A(2,2),B(2,−1),C(−1,−1),D(−1,2)A(2,2), B(2,-1), C(-1,-1), D(-1,2)A(2,2),B(2,−1),C(−1,−1),D(−1,2), then find its perimeter and area.

Problem 15

Find the area of the triangle with vertices (4,4)(4,4)(4,4), (4,0)(4,0)(4,0), and (0,0)(0,0)(0,0) by counting whole and half squares. 8 sq. units. Which quadrant is the point (−3,2)(-3,2)(−3,2) in? Second.

Problem 16

Triunghiul echilateral ABCABCABC are perimetrul 27 cm27 \mathrm{~cm}27 cm. Găsește lungimea segmentului MCMCMC, unde AN=6 cmAN=6 \mathrm{~cm}AN=6 cm.

Problem 17

Identify a function that fits the points (−2,8)(-2, 8)(−2,8), (1,5)(1, 5)(1,5), (3,13)(3, 13)(3,13), and (5,29)(5, 29)(5,29).

Problem 18

Graph the inequality 10>x≥110 > x \geq 110>x≥1 on a number line.

Problem 19

Graph the piecewise function: f(x)={4for x≤−1x+3for −1<x<42x−2for x≥4 f(x) = \begin{cases} 4 & \text{for } x \leq -1 \\ x + 3 & \text{for } -1 < x < 4 \\ 2x - 2 & \text{for } x \geq 4 \end{cases} f(x)=⎩⎨⎧​4x+32x−2​for x≤−1for −1<x<4for x≥4​

Problem 20

5. Într-un dreptunghi cu AB=12 cmAB=12 \mathrm{~cm}AB=12 cm și BC=4 cmBC=4 \mathrm{~cm}BC=4 cm, calculează aria triunghiului CEOCEOCEO și unghiul BFCBFCBFC.

Problem 21

Calculate the distance BCBCBC in triangle ABCABCABC where AB=1.5 kmAB=1.5 \text{ km}AB=1.5 km, AC=1.2 kmAC=1.2 \text{ km}AC=1.2 km, and ∠A=50∘\angle A=50^\circ∠A=50∘.

Problem 22

Find T(1)T(1)T(1) from the graph, explain its meaning, and determine when the temperature reaches 70∘F70^{\circ} \mathrm{F}70∘F.

Problem 23

Find two consecutive whole numbers that 78\sqrt{78}78​ is between and justify your answer.

Problem 24

Zeichne den Graphen für Anettes Inlinerfahrt: Ampelhalt, steiniger Weg, Auto vorlassen, dann Ankunft.

Problem 25

Der Bus fährt um 8.05 Uhr ab. a) Zeichne den Graphen. b) Wann ist die Endstation erreicht? c) Wie lang ist die Strecke?

Problem 26

Graph the function defined by f(x)=x+5f(x) = x + 5f(x)=x+5.

Problem 27

Draw the parabola y=3(x+3)2+4y=3(x+3)^{2}+4y=3(x+3)2+4, indicating the vertex and where it intersects the axes.

Problem 28

Sketch the graphs of these equations and their intercepts: 1. y=−(x−3)2+4y=-(x-3)^{2}+4y=−(x−3)2+4 2. y=12(x+2)2+2y=\frac{1}{2}(x+2)^{2}+2y=21​(x+2)2+2 3. y=3(x+3)2+4y=3(x+3)^{2}+4y=3(x+3)2+4 4. y=−2(x−1)2+2y=-2(x-1)^{2}+2y=−2(x−1)2+2

Problem 29

Find the slope between points (0,2) and (8,13). Which describes the temperature change per minute: 3.25∘C3.25^{\circ} \mathrm{C}3.25∘C, 5.25∘C5.25^{\circ} \mathrm{C}5.25∘C, 1.25∘C1.25^{\circ} \mathrm{C}1.25∘C, or 7.25∘C7.25^{\circ} \mathrm{C}7.25∘C?

Problem 30

Graph Fran's weekly earnings ($480\$ 480$480 for 40 hours, 181818 for each hour over) if she works hhh hours over 40.

Problem 31

Calculate the distance BCBCBC in triangle ABCABCABC where AB=1.5AB=1.5AB=1.5 km, AC=1.2AC=1.2AC=1.2 km, and A^=50∘\hat{A}=50^\circA^=50∘.

Problem 32

Graph the line given by the equation y=x−2y=x-2y=x−2.

Problem 33

Can nonadjacent angles share vertex AAA and arm ABA BAB? If yes, provide an example; if no, explain why.

Problem 34

A blue whale swims 2.5 miles in 5 minutes. Create a graph of distance vs. time. How far does it swim in 1 minute?

Problem 35

Help Milynn find the center of the next circle for her inscribed triangle. Consider previous circles, rules, and vertex positions.

Problem 36

Sketch the graph of the function y=3.2x+1−1y=3.2^{x+1}-1y=3.2x+1−1.

Problem 37

Find the slope between points (0,0) and (1,30) on the line. Can you find another pair of points with a different slope?

Problem 38

A marine biologist studies a dolphin's speed. It swims 55 meters in 5 seconds. Graph the distance over time. How far in 1 second?

Problem 39

Find the slope of the line for the points (1,10) to (2,20) and for (1,10) to (5,50). What does it represent?

Problem 40

Graph the line given by the equation y+2=2(x+1)y + 2 = 2(x + 1)y+2=2(x+1). Select points on the graph and submit.

Identify the quadrilateral formed by the points $(-5,0),(0,4),(5,0),(0,-4)$ . Options: A. Trapezoid B. Rhombus C. Square D. Rectangle.

Sketch the curves $y=x^{2}+x$ and $y=-2 \cdot x^{2}+4$ from $x=0$ to $x=2$ . Find the area between them using integrals.

Determine which statement is true for the function $f(x)=a\left(2^{x}\right)$ given the values of $a$ and $f(0)$ or $f(1)$ .

Graph $g(x)=|x-2|$ and compare it to $f(x)=|x|$ . Describe the domain and range. Select the correct translation and range.

Graph $g(x)=-\frac{1}{4}|x|$ . Compare to $f(x)=|x|$ and describe domain and range. Choose the correct option.

מצא את הגרף של הפונקציה $f(x)=\sqrt{3-x}$ .

Graph the intervals $P=(-\infty, 7)$ , $Q=[-3,4]$ , and $R=(2, \infty)$ . Find $P \cup Q$ , $Q \cap R$ , and $P \cap R'$ .

What is the initial height of a tennis ball dropped from 17.4 cm after $t$ seconds?

What is the football's greatest height if it reaches 4.9 meters at time $t=1$ ?

What is the initial height of a tennis ball dropped from a height of $176.4$ cm at time $t=0$ ?

Find the coordinates of the minimum point of the graph of $x^{2}-7x+11$ .

Locate points of rectangle $ABCD$ at $A(2,2), B(2,-1), C(-1,-1), D(-1,2)$ , then find its perimeter and area.

Find the area of the triangle with vertices $(4,4)$ , $(4,0)$ , and $(0,0)$ by counting whole and half squares. 8 sq. units. Which quadrant is the point $(-3,2)$ in? Second.

Triunghiul echilateral $ABC$ are perimetrul $27 \mathrm{~cm}$ . Găsește lungimea segmentului $MC$ , unde $AN=6 \mathrm{~cm}$ .

Identify a function that fits the points $(-2, 8)$ , $(1, 5)$ , $(3, 13)$ , and $(5, 29)$ .

Graph the inequality $10 > x \geq 1$ on a number line.

Graph the piecewise function: $f(x) = \begin{cases} 4 & \text{for } x \leq -1 \\ x + 3 & \text{for } -1 < x < 4 \\ 2x - 2 & \text{for } x \geq 4 \end{cases}$

5. Într-un dreptunghi cu $AB=12 \mathrm{~cm}$ și $BC=4 \mathrm{~cm}$ , calculează aria triunghiului $CEO$ și unghiul $BFC$ .

Calculate the distance $BC$ in triangle $ABC$ where $AB=1.5 \text{ km}$ , $AC=1.2 \text{ km}$ , and $\angle A=50^\circ$ .

Find $T(1)$ from the graph, explain its meaning, and determine when the temperature reaches $70^{\circ} \mathrm{F}$ .

Find two consecutive whole numbers that $\sqrt{78}$ is between and justify your answer.

Graph the function defined by $f(x) = x + 5$ .

Draw the parabola $y=3(x+3)^{2}+4$ , indicating the vertex and where it intersects the axes.

Sketch the graphs of these equations and their intercepts:
1. $y=-(x-3)^{2}+4$
2. $y=\frac{1}{2}(x+2)^{2}+2$
3. $y=3(x+3)^{2}+4$
4. $y=-2(x-1)^{2}+2$

Find the slope between points (0,2) and (8,13). Which describes the temperature change per minute: $3.25^{\circ} \mathrm{C}$ , $5.25^{\circ} \mathrm{C}$ , $1.25^{\circ} \mathrm{C}$ , or $7.25^{\circ} \mathrm{C}$ ?

Graph Fran's weekly earnings ( $\$ 480$ for 40 hours, $18$ for each hour over) if she works $h$ hours over 40.

Calculate the distance $BC$ in triangle $ABC$ where $AB=1.5$ km, $AC=1.2$ km, and $\hat{A}=50^\circ$ .

Graph the line given by the equation $y=x-2$ .

Can nonadjacent angles share vertex $A$ and arm $A B$ ? If yes, provide an example; if no, explain why.

Sketch the graph of the function $y=3.2^{x+1}-1$ .

Graph the line given by the equation $y + 2 = 2(x + 1)$ . Select points on the graph and submit.

Graph the function $y=\frac{1}{x+2}+2$ .

Create a system of equations with infinite solutions by graphing a line parallel to $y=-3x-4$ and provide its equation.

Sketch the graph of $y=3x^{2}-6x+5$ for $0 \leq x \leq 4$ . Identify turning point, intercepts, and state the range of $y$ .

Sketch the graph of $f(x)=\frac{3}{x+1}+2$ . Include all 6 axis intersections and asymptotes.

Rhianna claims different functions can share $x$ -intercepts $(-5,0),(2,0),(6,0)$ , domain $[-5,7]$ , and range $[-4,10]$ . Can you find examples?

Choose the graph of the function $h(x)=\frac{1}{3} x^{2}$ and its parent function.

Plot the points $(-4,1)$ and $(1,-1.5)$ on the coordinate plane. Click to add or remove points.

Approximate the average rate of change of infections from 0 to 8 days after April 1, 2020, using $P(8) \approx 5.55$ .

Approximate the average rate of change of infections from 0 to 8 days after April 1, 2020, using $P(8) - P(0)$ .

Graph the line $-3y = x - 3$ by plotting at least two points on the axes. Use technology to assist you.

Plot several terms of the logistic equation $x_{t+1}=c x_{t}(1-x_{t})$ with $x_{0}=0.4$ and $c=3.5$ .

Dibuja un histograma de los tiempos de pago: $19,15,43,39,35,31,27,22,18,14,42,38,13,13,13,41,41,41,37,37,37,33$ . Usa límites de clase 12.5 y ancho 7.

Calculate the average rates of change for COVID-19 infections in Minnesota over these intervals using $\frac{\Delta y}{\Delta x}$ :
1. 0 to 8 days: (calculate)
2. 8 to 16 days: 0.59 thousand/day
3. 0 to 16 days: 0.46 thousand/day

Draw the angle $150^{\circ}$ , find its reference angle, and identify the quadrant of its terminal side.

Graph the function $y=x^{3}$ .

Find the average rate of change of the function $f(x)=x^{2}+6x+10$ over the interval $[-2,1]$ .

Sketch a function with a negative average rate of change on the interval $[0,3]$ .

Plot the points $\left\{\frac{3}{4}, 0, -\frac{5}{4}, -0.5, 1.5\right\}$ on a number line.

Graphically analyze if the function $g(x)=x^{3}-x$ is even, odd, or neither.

Graph the line through the point $(-4,-3)$ with slope $m=4$ .

Graph the line through the point $(-3,-5)$ with a slope of $m=3$ .

Graph Jeriel's temperature data starting at $56^{\circ} \mathrm{F}$ , rising and falling over the day, ending at $60^{\circ}$ .

Graph the piecewise function: $f(x)=\begin{cases} 3, & -\infty<x\leq-1 \\ x-3, & -1<x\leq2 \\ x/2, & 2<x\leq\infty \end{cases}$

Graph the distance from home after $x$ hours for a trip to a park 20 miles away at $40 \mathrm{mph}$ , 2 hours at the park, then return at $20 \mathrm{mph}$ .