Deck 3: Graphs and Functions

Question 1

Determine the quadrant in which the point is located without plotting the point. $\left( \frac { 19 } { 10 } , - \frac { 5 } { 6 } \right)$

A)Quadrant III
B)Quadrant IV
C)Quadrant I
D)Quadrant II

Answer 1

Quadrant IV

Question 2

Plot the points on a rectangular coordinate system. $( 2,4 ) , ( - 2 , - 4 )$

A)
B)
C)
D)
E)

Answer 2

Question 3

Find the distance between $( - 9,7 )$ and $( 11 , - 4 )$ . Round your answer to two decimal places.

A) 19.72
B) 45.65
C) 3.61
D) 22.83
E) 11.87

Answer 3

22.83

Question 4

Determine the coordinates of the point labeled 2 .

A) $( 3 , - 2 )$
B) $( - 3,2 )$
C) $( 3,2 )$
D) $( - 2 , - 3 )$
E) $( 2,3 )$

Question 5

Determine all possible quadrants in which the point can be located. Assume $x \neq 0$ and $y \neq 0$ . $( x , y ) , x + y < 0$

A)Quadrants $\text { II, III and IV }$
B)Quadrants II and III
C)Quadrants $\text { I, II and IV }$
D)All quadrants
E)Quadrants I and II

Question 6

A right triangle has vertices at $A ( - 4,3 ) , B ( 3,5 )$ and $C ( 5 , - 2 )$ . Find the length of the three line segments, AB , BC , AC . Round your answer to two decimal places.

A) $A B = 8.06 , B C = 7.28 , A C = 10.30$
B) $A B = 8.06 , B C = 9.43 , A C = 10.30$
C) $A B = 7.28 , B C = 7.28 , A C = 1.41$
D) $A B = 7.28 , B C = 9.43 , A C = 10.30$
E) $A B = 7.28 , B C = 7.28 , A C = 10.30$

Question 7

Find the distance between $\left( \frac { 3 } { 4 } , 4 \right)$ and $\left( \frac { 3 } { 4 } , - 8 \right)$ .

A) 4
B) 24
C) $12 \frac { 3 } { 4 }$
D) 12
E) $4 \frac { 3 } { 4 }$

Question 8

Find the coordinates of the point located 9 units to the right of the y -axis and 2 units above the x -axis.

A) $( - 9,2 )$
B) $( - 2,9 )$
C) $( 9 , - 2 )$
D) $( - 9 , - 2 )$
E) $( 9,2 )$

Question 9

Plot the points on a rectangular coordinate system. $\left( - \frac { 3 } { 2 } , - \frac { 5 } { 2 } \right) , ( 1,0 )$

A)
B)
C)
D)
E)

Question 10

Plot the points $( 1,4 ) , ( 2,0 ) , ( 5,5 )$ and connect them with line segments to form a figure.

A)
B)
C)
D)
E)

Question 11

Use the Distance Formula to determine whether the points $( 7,9 ) , ( 7,4 )$ and $( 7,7 )$ are collinear.

A) $\text { not collinear }$
B) $\text { collinear }$

Question 12

Find the perimeter of the triangle with the vertices $( - 4,0 ) , ( 0,8 )$ and $( 1,0 )$ . Round your answer to two decimal places.

A) 17.71
B) 22.01
C) 24.71
D) 18.01
E) 19.71

Question 13

Find the coordinates of the vertices of the figure if it is shifted 3 units to the right and 3 units up.

A) $( 8,5 ) , ( 0,8 ) , ( 2,5 ) , ( 0,1 )$
B) $( 8,1 ) , ( - 3,8 ) , ( 2,3 ) , ( - 3 , - 3 )$
C) $( - 2,5 ) , ( 0,3 ) , ( 2,3 ) , ( 0,1 )$
D) $( - 2,5 ) , ( 0,8 ) , ( 4,1 ) , ( 6,5 )$
E) $( - 2,5 ) , ( 0,8 ) , ( 2,5 ) , ( 0,1 )$

Question 14

Determine all possible quadrants in which the point can be located. Assume $y \neq 0$ . $( - 3 , y )$ y is a real number

A)Quadrants I and II
B)Quadrants III and IV
C)Quadrants IV and I
D)Quadrants II and III
E)Quadrants II and IV

Question 15

Plot the points $( 0,2 ) , ( 0 , - 1 ) , ( - 3 , - 1 )$ and $( - 3,2 )$ . Find the square that is obtained by connecting the points with line segments.

A)
B)
C)
D)
E)

Question 16

Find the coordinates of the point located 2 units to the left of the y -axis and 9 units above the x -axis.

A) $( 2 , - 9 )$
B) $( - 2 , - 9 )$
C) $( - 9,2 )$
D) $( - 2,9 )$
E) $( 2,9 )$

Question 17

Determine which of the ordered pairs is a solution of the equation. $x + 6 y - 4 = 0$

A) $\left( 2 , \frac { 1 } { 6 } \right)$
B) $\left( 3 , \frac { 1 } { 3 } \right)$
C) $\left( 1 , \frac { 1 } { 3 } \right)$
D) $\left( 2 , \frac { 1 } { 3 } \right)$
E) $\left( 1 , \frac { 1 } { 6 } \right)$

Question 18

Plot the points $( 0,0 ) , ( 0 , - 3 ) , ( 2 , - 1 )$ and $( 2 , - 4 )$ . Find the parallelogram that is obtained by connecting the points with line segments.

A)
B)
C)
D)
E)

Question 19

Determine which of the ordered pairs is a solution of the equation. $y = \frac { 8 } { 3 } x + 2$

A) $( - 7 , - 12 )$
B) $( - 7 , - 15 )$
C) $( - 6 , - 14 )$
D) $( - 5 , - 16 )$
E) $( - 6 , - 16 )$

Question 20

Determine the quadrant in which the point is located without plotting the point. $( 34 , - 21 )$

A)Quadrant III
B)Quadrant II
C)Quadrant I
D)Quadrant IV

Question 21

Find the x- and y- intercepts, if any, of $y = | x | - 2$ .

A)x- intercept at 0 , y- intercept at -2
B)x- intercept at $\pm 2$ , y- intercept at 2
C)x- intercept at -2 , y- intercept at -2
D)x- intercept at $\pm 2$ , y- intercept at -2
E)no intercepts

Question 22

Find the x - and y -intercepts of the graph of the equation $y = 7 x + 9$ .

A)x -intercept: $\frac { 9 } { 7 }$ y -intercept: 9
B)x -intercept: - $\frac { 9 } { 7 }$ y -intercept: 9
C)x -intercept: -7 y -intercept: 9
D)x -intercept: 7 y -intercept: 9
E)x -intercept: 9 y -intercept: $\frac { 9 } { 7 }$

Question 23

Graph the equation $3 x + 2 y = 10$ .

A)
B)
C)
D)
E)

Question 24

Find the midpoint of the line segment joining the points $( - 6,0 )$ and $( 8,4 )$ .

A) $( 14,4 )$
B) $( 1,4 )$
C) $( 7,2 )$
D) $( 1,2 )$
E) $( 2,4 )$

Question 25

Estimate the x - and y -intercepts of the graph.

A)x -intercept: y -intercept:
B)x -intercept: y -intercept:
C)x -intercept: y -intercept:
D)x -intercept: y -intercept:
E)x -intercept: y -intercept:

Question 26

Sketch the graph of the equation $y = \frac { 2 } { 3 } x - 2$ and label three points on the graph.

A)
B)
C)
D)
E)

Question 27

Graph the equation $y = 2 - x$ .

A)
B)
C)
D)
E)

Question 28

Match the correct equation with the given graph.

A) $y = 2 + x$
B) $y = - 2 + x$
C) $y = - 2 x$
D) $y = - 2 - x$
E) $y = 2 - x$

Question 29

Use a graphing calculator (with a standard viewing window)to graph the equation $y = - \frac { 1 } { 2 } x ^ { 2 } + 1$ .

A)
B)
C)
D)
E)

Question 30

Graphically estimate the x- and y- intercepts, if any, of the graph.

A)x- intercept at , y- intercept at
B)x- intercept at , no y- intercepts
C)no x- intercepts, y- intercept at
D)x- intercept at , y- intercept at
E)no intercepts

Question 31

Compete the table and use the results to sketch the graph of the equation $y = | x - 1 |$ .
$\begin{array} { | l | l | l | l | l | l | } \hline x & - 2 & - 1 & 0 & 1 & 2 \\\hline y & & & & & \\\hline\end{array}$

A)
B)
C)
D)
E)

Question 32

Use a graphing calculator (with a standard viewing window)to graph the equation $y = 3 - | x + 2 |$ .

A)
B)
C)
D)
E)

Question 33

Match the correct equation with the given graph.

A) $y = 2 - x ^ { 2 }$
B) $y = 2 + x ^ { 2 }$
C) $y = - 2 - x ^ { 2 }$
D) $y = - 2 x ^ { 2 }$
E) $y = - 2 + x ^ { 2 }$

Question 34

A football quarterback throws a pass from the -yardline, yards from the sideline. The pass is caught by the wide receiver at the -yardline, yards from the same sideline. How long is the pass (in yards)? Round your answer to two decimal places.

A) yards
B) yards
C) yards
D) yards
E) yards

Question 35

Find the x - and y -intercepts of the graph of the equation $- 2 x - 4 y - 56 = 0$ .

A)x -intercept: 2 y -intercept: 4
B)x -intercept: 28 y -intercept: -14
C)x -intercept: -14 y -intercept: 28
D)x -intercept: 14 y -intercept: 28
E)x -intercept: -28 y -intercept: -14

Question 36

Graph the equation $y = - | x | + 6$ .

A)
B)
C)
D)
E)

Question 37

Compete the table and use the results to sketch the graph of the equation $y = x ^ { 2 } - 1$
$\begin{array} { | l | l | l | l | l | l | } \hline x & - 2 & - 1 & 0 & 1 & 2 \\\hline y & & & & & \\\hline\end{array}$

A)
B)
C)
D)
E)

Question 38

Find the x- and y- intercepts, if any, of $y = 18 - \frac { 2 } { 5 } x$ .

A)x- intercept at -45 , y- intercept at 18
B)x- intercept at 18 , y- intercept at 45
C)x- intercept at 45 , y- intercept at 18
D)x- intercept at -18, y- intercept at 45
E)no intercepts

Question 39

Estimate the x - and y -intercepts of the graph.

A)x -intercept: , y -intercept:
B)x -intercept: y -intercept: ,
C)x -intercept: y -intercept:
D)x -intercept: y -intercept: ,
E)x -intercept: , y -intercept:

Question 40

Find the x- and y- intercepts, if any, of $y = | x - 3 | - 7$ .

A)x- intercept at $\pm 7$ , y- intercept at -7
B)x- intercept at -7 , y- intercept at -7
C)x- intercept at 10 , -4 , y- intercept at -4
D)x- intercept at $\pm 3$ , y- intercept at $7$
E)no intercepts

Question 41

Sketch the graph of $y = 4 x + 8$ .

A)
B)
C)
D)
E)

Question 42

Use the formula for slope to find the value of y such that the line through the points (1,-4) and (0,y) has slope of m=-2 .

A) y=4
B) y=-4
C) y=-2
D) y=2
E) $y = 5$

Question 43

Find the slope (if possible)of the line passing through the points $\left( \frac { 4 } { 5 } , - \frac { 7 } { 8 } \right)$ and $\left( - \frac { 5 } { 3 } , - 6 \right)$ .

A) $\frac { 296 } { 615 }$
B) $\frac { 615 } { 296 }$
C) - $\frac { 615 } { 296 }$
D) - $\frac { 296 } { 615 }$
E)not possible

Question 44

Find the slope (if possible)of the line passing through the points (-6,2) and $( - 7 , - 6 )$ .

A) $- \frac { 1 } { 8 }$
B)8
C)-8
D) $\frac { 1 } { 8 }$
E)not possible

Question 45

Find the slope of the line passing through points $\left( \frac { 3 } { 4 } , 7 \right)$ and $\left( 7 , - \frac { 1 } { 2 } \right)$ .

A) $- \frac { 6 } { 5 }$
B) $\frac { 6 } { 5 }$
C) $\frac { 26 } { 25 }$
D) - $\frac { 26 } { 25 }$
E) 5

Question 46

Sketch the graph of the equation $y = x ^ { 2 } - 1$ and label three points on the graph.

A)
B)
C)
D)
E)

Question 47

A manufacturing plant purchases a new molding machine for $\$ 950,000$ . The depreciated value y after t years is given by $y = 950,000 - 20,000 t$ , $0 \leq t \leq 8$ . Sketch the graph of this model.

A)
B)
C)
D)
E)

Question 48

Identify the line in the figure that has slope .

A)
B)
C)
D)
E)none

Question 49

State if the line passing through the points $( 0,8 )$ and $( - 4,10 )$ rises, falls, is horizontal, or is vertical.

A)The line passing through the points $( 0,8 )$ and $( - 4,10 )$ falls.
B)The line passing through the points $( 0,8 )$ and $( - 4,10 )$ vertical.
C)The line passing through the points $( 0,8 )$ and $( - 4,10 )$ horizontal.
D)The line passing through the points $( 0,8 )$ and $( - 4,10 )$ rises.

Question 50

Sketch the graph of the equation $y = - | x | + 1$ and label three points on the graph.

A)
B)
C)
D)
E)

Question 51

Sketch the graph of the line $3 x - 9 y = 18$ . Then find the slope of the line.

A) $\text { Slope: } - \frac { 1 } { 4 }$
B)
$\text { Slope: } \frac { 1 } { 3 }$
C) $\text { Slope: } \frac { 1 } { 3 }$
D) $\text { Slope: } \frac { 1 } { 4 }$
E) $\text { Slope: } \frac { 1 } { 3 }$

Question 52

The table shows the projected number N (in millions)of persons with pets in a certain country. $$\begin{array} { | c | c | c | c | c | } \hline \text { Year } & 2010 & 2015 & 2020 & 2025 \\\hline N & 39.15 & 47.8 & 56.81 & 65.96 \\\hline\end{array}$$ A model for this data is $N = 1.83 t + 20.9$ where t represents time in years, with $t = 10$ corresponding to the year 2010. According to the model, in what year will the number of pet owners exceed $72.14$ million?

A) $2034$
B) $2029$
C) $2024$
D) $2027$
E) $2028$

Question 53

State if the line passing through the points $\left( \frac { 3 } { 4 } , 9 \right)$ and $\left( 6 , - \frac { 5 } { 2 } \right)$ rises, falls, is horizontal, or is vertical.

A)The line passing through the points $\left( \frac { 3 } { 4 } , 9 \right)$ and $\left( 6 , - \frac { 5 } { 2 } \right)$ rises.
B)The line passing through the points $\left( \frac { 3 } { 4 } , 9 \right)$ and $\left( 6 , - \frac { 5 } { 2 } \right)$ horizontal.
C)The line passing through the points $\left( \frac { 3 } { 4 } , 9 \right)$ and $\left( 6 , - \frac { 5 } { 2 } \right)$ falls.
D)The line passing through the points $\left( \frac { 3 } { 4 } , 9 \right)$ and $\left( 6 , - \frac { 5 } { 2 } \right)$ vertical.

Question 54

Your company purchases a new delivery van for $\$ 40,000$ . For tax purposes, the van will be depreciated over a seven year period. At the end of seven years, the value of the van is expected to be $5000 . The equation relating the depreciated value of the van, y , to the number of years, t , since it was purchased is given by $y = 40,000 - 5000 t$ . Sketch a graph of this equation.

A)
B)
C)
D)
E)

Question 55

State if the line passing through the points $( - 8 , - 9 )$ and $( - 2,6 )$ rises, falls, is horizontal, or is vertical.

A)The line passing through the points $( - 8 , - 9 )$ and $( - 2,6 )$ vertical.
B)The line passing through the points $( - 8 , - 9 )$ and $( - 2,6 )$ horizontal.
C)The line passing through the points $( - 8 , - 9 )$ and $( - 2,6 )$ rises.
D)The line passing through the points $( - 8 , - 9 )$ and $( - 2,6 )$ falls.

Question 56

Sketch the graph of $y = - x ( x + 4 )$ .

A)
B)
C)
D)
E)

Question 57

Find the slope of the line passing through points (0,0) and (-5,-8) .

A) $- \frac { 8 } { 5 }$
B) $- \frac { 5 } { 8 }$
C) $\frac { 3 } { 8 }$
D) $\frac { 5 } { 8 }$
E) $\frac { 8 } { 5 }$

Question 58

Your company purchases a new delivery van for $\$ 72,000$ . For tax purposes, the van will be depreciated over a seven year period. At the end of seven years, the value of the van is expected to be $9000 . The graph relating the depreciated value of the van, y , to the number of years, t , since it was purchased is shown below. What is the y- intercept of the graph, if any?

A) 53,000
B) 72,000
C) $12,160$
D) $23,800$
E)no y- intercept

Question 59

Your company purchases a new delivery van for $\$ 56,000$ . For tax purposes, the van will be depreciated over a seven year period. At the end of seven years, the value of the van is expected to be $7000 . Find a linear equation that relates the depreciated value of the van, y , to the number of years, t , since it was purchased.

A) $y = 56,000 + 7000 t$
B) $y = 7000 - 56,000 t$
C) $y = 56,000 - 49,000 t$
D) $y = 49,000 - 7000 t$
E) $y = 56,000 - 7000 t$

Question 60

Estimate the slope of the line from the graph given below.

A)-3
B)-2
C) $\frac { 1 } { 3 }$
D) - $\frac { 1 } { 3 }$
E)2

Question 61

Write the equation of the line that passes through the point (1,-1) and has slope m=5 . Write the equation in general form.

A) $- 5 x + y - 4 = 0$
B) $- 5 x + y + 6 = 0$
C) $5 x + y - 4 = 0$
D) $x + 5 y + 6 = 0$
E) $5 x + y + 6 = 0$

Question 62

Write the equation of the line that passes through the point $\left( 0 , - \frac { 7 } { 9 } \right)$ and has slope $m = - \frac { 9 } { 4 }$ . Write the equation in general form.

A) $81 x - 36 y + 28 = 0$
B) $81 x + 36 y + 28 = 0$
C) $81 x + 36 y + 7 = 0$
D) $36 x + 81 y - 28 = 0$
E) $36 x + 81 y - 7 = 0$

Question 63

Match the equation $y = \frac { 3 } { 2 } \pi + 3$ with its graph.

A)
B)
C)
D)
E)

Question 64

Sketch the graph of the line $- 3 x + 2 y + 6 = 0$ by plotting the x - and y -intercepts.

A)
B)
C)
D)
E)

Question 65

Determine whether the lines $L _ { 1 } : y = - \frac { 1 } { 2 } x - 3$ and $L _ { 2 } : y = - \frac { 1 } { 2 } x + 4$ are parallel, perpendicular, or neither.

A)neither
B)parallel
C)perpendicular

Question 66

Use the formula for slope to find the value of y such that the line through the points (-2,2) and (1,y) has slope of m= $- \frac { 8 } { 3 }$ .

A) y=-2
B) y=2
C) y=6
D) y=5
E) $y = - 6$

Question 67

Determine which of the lines $L _ { 1 } , L _ { 2 }$ and $L _ { 3 }$ passing through the indicated pairs of points are parallel.
$\begin{array} { |l|l|} \hline L _ { 1 } & ( - 2 , - 7 ) , ( 0,1 )\\\hline{ L _ { 2 } }&(-2,11),(5,-24) \\\hline{ L _ { 3 } } &(0,-2),(5,18)\\\hline\end{array}$

A) $L _ { 1 } \text { and } L _ { 3 }$
B) $L _ { 1 } \text { and } L _ { 2 }$
C) $L _ { 2 } \text { and } L _ { 3 }$
D)all are parallel
E)none are parallel

Question 68

Determine which of the lines $L _ { 1 } , L _ { 2 }$ and $L _ { 3 }$ passing through the indicated pairs of points are perpendicular.
$\begin{array} { | l | l | } \hline L _ { 1 } &\left(-1, \frac{4}{3}\right),\left(1, \frac{2}{3}\right)\\\hline L _ { 2 } &\left(1,-\frac{7}{6}\right),\left(4,-\frac{5}{3}\right) \\\hline L _ { 3 }& (-1,-4),(4,11) \\\hline\end{array}$

A) $L _ { 2 } \text { and } L _ { 3 }$
B) $L _ { 1 } \text { and } L _ { 2 }$
C) $L _ { 1 } \text { and } L _ { 3 }$
D)all are perpendicular
E)none are perpendicular

Question 69

Write the equation $12 x - 4 y + 5 = 0$ in slope-intercept form.

A) $y = - 3 x - \frac { 5 } { 4 }$
B) $y = 3 x + \frac { 5 } { 4 }$
C) $y = \frac { 1 } { 3 } x + \frac { 5 } { 4 }$
D) $y = - \frac { 1 } { 3 } x - \frac { 5 } { 4 }$
E) $y = 3 x - 5$

Question 70

The point (1,2) is on a line with undefined slope. Find two additional points on the line.

A) (2,1) and (0,3)
B) (1,0) and (1,0)
C) (2,3) and (0,1)
D) (2,1) and $( 0,2 )$
E) $( 1,3 )$ and $( 1,1 )$

Question 71

Write $8 x - 6 y + 1 = 0$ in slope-intercept form.

A) $y = \frac { 4 } { 3 } x + \frac { 1 } { 6 }$
B) $y = \frac { 3 } { 4 } x + \frac { 1 } { 6 }$
C) $y = \frac { 4 } { 3 } x - \frac { 1 } { 6 }$
D) $y = - \frac { 4 } { 3 } x + \frac { 1 } { 6 }$
E) $y = \frac { 4 } { 3 } x + 1$

Question 72

Write $x - 0.25 y - 2 = 0$ in slope-intercept form.

A) $y = 4 x - 2$
B) $y = - 4 x - 8$
C) $y = - 4 x + 8$
D) $y = - 0.25 x - 2$
E) $y = 4 x - 8$

Question 73

Write an equation of the line that passes through $\left( - 8 , \frac { 5 } { 2 } \right)$ and has a slope of $m = \frac { 1 } { 6 }$ .

A) $- x + 6 y = - 38$
B) $- x + y = - 38$
C) $x + 6 y = - 41$
D) $- x + 6 y = 23$
E) $- x + 6 y = - 23$

Question 74

Write the equation $x - 3 y + 6 = 0$ in slope-intercept form.

A) $y = - \frac { 1 } { 3 } x + 2$
B) $y = \frac { 1 } { 3 } x + 2$
C) $y = - 3 x - 2$
D) $y = 3 x - 2$
E) $y = - 3 x + 2$

Question 75

Write an equation in slope-intercept form of the line that passes through the point (0,9) and has a slope of $m = \frac { 1 } { 5 }$ .

A) $y = \frac { 1 } { 5 } x + 9$
B) $y = \frac { 1 } { 5 } x + \frac { 5 } { 9 }$
C) $y = \frac { 1 } { 5 } x - 9$
D) $y = \frac { 1 } { 5 } x + \frac { 9 } { 5 }$
E) $y = - \frac { 1 } { 5 } x + 9$

Question 76

Sketch the graph of the line through the point (1, 2)with slope .

A)
B)
C)
D)
E)

Question 77

An access ramp to a freeway extends horizontally a distance of 280 feet while it rises a total of 10 feet. Find the slope of the access ramp.

A)270
B) $\frac { 1 } { 28 }$
C) 28
D)290
E) $\frac { 29 } { 28 }$

Question 78

The slope, or pitch, of a roof is such that is rises (or falls)6 feet for every 5 feet of horizontal distance. Determine the maximum height of the attic for a 30-foot wide house. Round your answer to two decimal places.

A)36.00 feet
B)12.50 feet
C)15.00 feet
D)19.20 feet
E)18.00 feet

Question 79

State the slope and a point on the graph for the point-slope equation $y - 7 = 6 ( x - 8 )$ .

A) 6 ; $( - 8 , - 7 )$
B) 6 ; $( 8,7 )$
C) 7 ; $( - 8 , - 7 )$
D) $7$ ; $( - 48 , - 7 )$
E) $6$ ; $( 7,6 )$

Question 80

The point (-4,-3) is on a line with slope 3. Find two additional points on the line.

A) (-3,0) and (-5,-6)
B) (-1,-2) and (-7,-4)
C) (-7,-4) and (-10,-4)
D) $( - 3 , - 6 )$ and $( - 5,0 )$
E) $( - 2,3 )$ and $( - 5 , - 9 )$