Deck 2: Linear and Quadratic Functions

Question 1

Determine whether the given function is linear or nonlinear.
$$\begin{array} { c | c } x & y = f ( x ) \\\hline 3 & 15 \\7 & 35 \\11 & 55 \\15 & 75\end{array}$$

A) linear
B) nonlinear

Answer 1

A

Question 2

Determine the average rate of change for the function.
$$F ( x ) = 10$$

A) 0
B) $\frac { 1 } { 10 }$
C) 10
D) $- 10$

Answer 2

A

Question 3

Use the slope and y-intercept to graph the linear function.
$$h ( x ) = - \frac { 1 } { 2 } x - 3$$

A)

B)

C)

D)

Answer 3

D

Question 4

Determine the slope and y-intercept of the function.
F(x) = 2

A) m = 0; b = 2
B) m = 2; b = 2
C) m = 0; b = 0
D) m = 2; b = 0

Question 5

Use the slope and y-intercept to graph the linear function.
A)

B)

C)

D)

Question 6

Determine the slope and y-intercept of the function.
p(x) = -x + 6

A) m = 0; b = 6
B) m =1; b = - 6
C) m = -1; b =6
D) m = -1; b = - 6

Question 7

Use the slope and y-intercept to graph the linear function.
A)

B)

C)

D)

Question 8

Use the slope and y-intercept to graph the linear function.
f(x) = 2x - 2 A)

B)

C)

D)

Question 9

Use the slope and y-intercept to graph the linear function.
$$G ( x ) = 4 x$$

A)

B)

C)

D)

Question 10

Use the slope and y-intercept to graph the linear function.
$$F ( x ) = \frac { 1 } { 2 } x$$

A)

B)

C)

D)

Question 11

Determine the average rate of change for the function.
f(x) = 9x + 5

A) 5
B) 9
C) -5
D) -9

Question 12

Use the slope and y-intercept to graph the linear function.
A)

B)

C)

D)

Question 13

Determine the slope and y-intercept of the function.
$$f ( x ) = - \frac { 1 } { 2 } x + 3$$

A) $m = 3 ; b = - \frac { 1 } { 2 }$
B) $m = \frac { 1 } { 2 } ; b = - 3$
$\mathrm { C } ) \mathrm { m } = - \frac { 1 } { 2 } ; \mathrm { b } = 3$
D) $\mathrm { m } = - 2 ; \mathrm { b } = - 3$

Question 14

Determine the slope and y-intercept of the function.
f(x) = 5x - 10

A) m = 5; b = 10
B) m = -5; b = -10
C) m = -5; b = 10
D) m = 5; b = -10

Question 15

Use the slope and y-intercept to graph the linear function.
$$f ( x ) = \frac { 3 } { 5 } x - 1$$

A)

B)

C)

D)

Question 16

Determine the slope and y-intercept of the function.
$$F ( x ) = \frac { 1 } { 4 } x$$

A) $\mathrm { m } = 0 ; \mathrm { b } = \frac { 1 } { 4 }$
B) $\mathrm { m } = 4 ; \mathrm { b } = 0$
C) $\mathrm { m } = \frac { 1 } { 4 } ; \mathrm { b } = 0$
D) $\mathrm { m } = - \frac { 1 } { 4 } ; \mathrm { b } = 0$

Question 17

Determine the average rate of change for the function.
p(x) = -x - 4

A) 1
B) 4
C) -1
D) -4

Question 18

Determine the average rate of change for the function.
h(x) = -7x - 2

A) - 2
B) 7
C) -7
D) 2

Question 19

Determine the slope and y-intercept of the function.
G(x) = -2x

A) m = 2; b = 0
B) m = -2; b = 0
C) m = 1 ; b = 0
D) m = 0; b = -2 - 2

Question 20

Determine the slope and y-intercept of the function.
h(x) = -11x - 10

A) m = -11; b = - 10
B) m = 11; b = - 10
C) m = -11; b = 10
D) m = 11; b = 10

Question 21

Graph the function. State whether it is increasing, decreasing, or constant..
A) increasing

B) decreasing

C) decreasing

D) increasing

Question 22

Graph the function. State whether it is increasing, decreasing, or constant..
A) decreasing

B) increasing

C) decreasing

D) increasing

Question 23

Find the zero of the linear function.
$$G ( x ) = - \frac { 1 } { 3 } x - 7$$

A) $- \frac { 7 } { 3 }$
B) 21
C) $- 21$
D) $\frac { 7 } { 3 }$

Question 24

Determine the average rate of change for the function.
$$f ( x ) = \frac { 2 } { 5 } x + 2$$

A) $\frac { 2 } { 5 }$
B) 2
C) $- \frac { 2 } { 5 }$
D) $- 2$

Question 25

Find the zero of the linear function.
g(x) = 6x - 30

A) -30
B) 0
C) -5
D) 5

Question 26

Find the zero of the linear function.
f(x) = 9x + 36

A) -4
B) 0
C) 36
D) 4

Question 27

Graph the function. State whether it is increasing, decreasing, or constant..
h(x) = -4x - 3 A) decreasing

B) increasing

C) increasing

D) decreasing

Question 28

Find the zero of the linear function.
f(x) = x + 8

A) 8
B) 0
C) -8
D) 16

Question 29

Graph the function. State whether it is increasing, decreasing, or constant..
A) decreasing

B) increasing

C) decreasing

D) increasing

Question 30

Graph the function. State whether it is increasing, decreasing, or constant..
A) increasing

B) increasing

C) increasing

D) decreasing

Question 31

Find the zero of the linear function.
h(x) = 13 - x

A) 1
B) -26
C) 13
D) -13

Question 32

Solve the problem.
Suppose that f(x) = -x - 9 and g(x) = x - 12. (a) Solve f(x) = 0.
(b) Solve g(x) = 0.
(c) Solve f(x) = g(x).

A) (a) x = -9; (b) x = -12; (c) x = 1.5
B) (a) x = 9; (b) x = 12; (c) x = 1.5
C) (a) x = -9; (b) x = 12; (c) x = 1.5
D) (a) x = -9; (b) x = 12; (c) x = -10.5

Question 33

Graph the function. State whether it is increasing, decreasing, or constant..
A) decreasing

B) constant

C) constant

D) constant

Question 34

Find the zero of the linear function.
$$h ( x ) = - 4 x + 5$$

A) $- \frac { 4 } { 5 }$
B) 1
C) $- 1$
D) $\frac { 5 } { 4 }$

Question 35

Determine the average rate of change for the function.
$$h ( x ) = - \frac { 1 } { 2 } x - 1$$

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

Question 36

Find the zero of the linear function.
$$F ( x ) = \frac { 1 } { 7 } x - 3$$

A) 21
B) $- 21$
C) $\frac { 3 } { 7 }$
D) $- \frac { 3 } { 7 }$

Question 37

Find the zero of the linear function.
g(x) = -x + 2

A) 0
B) -4
C) -2
D) 2

Question 38

Graph the function. State whether it is increasing, decreasing, or constant..
$$f ( x ) = \frac { 3 } { 4 } x + 1$$

A) decreasing

B) increasing

C) increasing

D) increasing

Question 39

Graph the function. State whether it is increasing, decreasing, or constant..
$$h ( x ) = - \frac { 3 } { 5 } x - 1$$

A) increasing

B) decreasing

C) decreasing

D) decreasing

Question 40

Solve the problem.
Suppose that f(x) = -x - 1 and g(x) = x - 14. (a) Solve f(x) > 0.
(b) Solve g(x) > 0.
(c) Solve f(x) ≤ g(x).

A) (a) x < -1; (b) x < -14; (c) x ≤6.5
B) (a) x > 1; (b) x > 14; (c) x > 6.5
C) (a) x < -1; (b) x > 14; (c) x ≥ 6.5
D) (a) x < -1; (b) x < 14; (c) x ≥ -7.5

Question 41

Plot a scatter diagram.
$$\begin{array} { l | l l l l l l l l l } \mathrm { x } & 18 & 25 & 29 & 47 & 59 & 67 & 74 & 83 & 85 \\\hline \mathrm { y } & 13 & 27 & 35 & 46 & 69 & 52 & 66 & 95 & 75\end{array}$$

A)

B)

C)

D)

Question 42

Solve the problem.
Let f(x) be the function represented by the dashed line and g(x) be the function represented by the solid line. Solve the equation f(x) ≥ g(x).

A) x < -1
B) x ≥ 1
C) x ≥ -1
D) x ≤1

Question 43

Solve the problem.
A lumber yard has fixed costs of $1384.90 per day and variable costs of $0.56 per board-foot produced. Lumber sells for $1.66 per board-foot. How many board-feet must be produced and sold daily to break even?

A) 623 board-feet
B) 2473 board-feet
C) 1259 board-feet
D) 839 board-feet

Question 44

Solve the problem.
Let f(x) be the function represented by the dashed line and g(x) be the function represented by the solid line. Solve the equation f(x) = g(x).

A) x = -4
B) x = 4
C) x = -3
D) x = 3

Question 45

Solve the problem.
To convert a temperature from degrees Celsius to degrees Fahrenheit, you multiply the temperature in degrees Celsius by 1.8 and then add 32 to the result. Express F as a linear function of c.

A) F(c) = 1.8 + 32c $$\text { B) } \mathrm { F } ( \mathrm { c } ) = \frac { \mathrm { c } - 32 } { 1.8 }$$
C) F(c) = 1.8c + 32
D) F(c) = 33.8c

Question 46

Solve the problem.
If an object is dropped from a tower, then the velocity, V (in feet per second), of the object after t seconds can be obtained by multiplying t by 32 and adding 10 to the result. Find V as a linear function of t, and use this
Function to evaluate V(2.2), the velocity of the object at time t = 2.2 seconds.

A) V(2.2) = 81.7 feet per second
B) V(2.2) = 79.7 feet per second
C) V(2.2) = 78.4 feet per second
D) V(2.2) = 80.4 feet per second

Question 47

Solve the problem.
Suppose that the quantity supplied S and quantity demanded D of baseball caps at a major league game are given by the functions S(p) = 3230 - 90p and D(p) = 100p, where p is the price. Find the equilibrium price for
Caps at the game. Then find the equilibrium quantity.

A) $32, $350
B) $10, $2330
C) $17, $1700
D) $10, $1700

Question 48

Solve the problem.
Linda needs to have her car towed. Little Town Auto charges a flat fee of $45 plus $3 per mile towed. Write a function expressing Linda's towing cost, c, in terms of miles towed, x. Find the cost of having a car towed 14
Miles.

A) c(x) = 3x + 45; $77
B) c(x) = 3x; $48
C) c(x) = 3x; $42
D) c(x) = 3x + 45; $87

Question 49

Solve the problem.
Regrind, Inc. regrinds used typewriter platens. The variable cost per platen is $1.50. The total cost to regrind 70 platens is $400. Find the linear cost function to regrind platens. If reground platens sell for $8.40 each, how
Many must be reground and sold to break even?

A) C(x) = 1.50x + 295; 30 platens
B) C(x) = 1.50x + 400; 41 platens
C) C(x) = 1.50x + 295; 43 platens
D) C(x) = 1.50x + 400; 58 platens

Question 50

Plot a scatter diagram.
$$\begin{array} { c | c c c c c c c c c c } \mathrm { x } & 22 & - 10 & 10 & - 11 & - 6 & 12 & 4 & 13 & 5 & - 4 \\\hline \mathrm { y } & 53 & 17 & 43 & - 15 & - 2 & 38 & 7 & 68 & - 4 & 3\end{array}$$ A)

B)

C)

D)

Question 51

Plot and interpret the appropriate scatter diagram.
The table shows the study times and test scores for a number of students. Draw a scatter plot of score versus
time treating time as the independent variable. $$\begin{array} { l | c c c c c c c c } \text { Study Time (min) } & 9 & 16 & 21 & 26 & 33 & 36 & 40 & 47 \\\hline \text { Test Score } & 59 & 61 & 64 & 65 & 73 & 74 & 78 & 78\end{array}$$

Question 52

Solve the problem.
In a certain city, the cost of a taxi ride is computed as follows: There is a fixed charge of $2.95 as soon as you get in the taxi, to which a charge of $1.60 per mile is added. Find an equation that can be used to determine the cost, C(x), of an x-mile taxi ride, and use this equation to find the cost of a 4-mile taxi ride.

A) $10.25
B) $9.23
C) $9.53
D) $9.35

Question 53

Solve the problem.
A truck rental company rents a moving truck one day by charging $29 plus $0.11 per mile. Write a linear equation that relates the cost C, in dollars, of renting the truck to the number x of miles driven. What is the cost
Of renting the truck if the truck is driven 180 miles?

A) C(x) = 0.11x + 29; $48.80
B) C(x) = 0.11x - 29; -$9.20
C) C(x) = 29x + 0.11; $5220.11
D) C(x) = 0.11x + 29; $30.98

Question 54

Solve the problem.
Marty's Tee Shirt & Jacket Company is to produce a new line of jackets with a embroidery of a Great Pyrenees dog on the front. There are fixed costs of $690 to set up for production, and variable costs of $28 per jacket. Write
An equation that can be used to determine the total cost, C(x), encountered by Marty's Company in producing x jackets, and use the equation to find the total cost of producing 121 jackets.

A) $4090
B) $4078
C) $4058
D) $4070

Question 55

Solve the problem.
Let f(x) be the function represented by the dashed line and g(x) be the function represented by the solid line. Solve the equation f(x) < g(x).

A) x < 1
B) x > -2
C) x > 1
D) x < -2

Question 56

Solve the problem.
Marty's Tee Shirt & Jacket Company is to produce a new line of jackets with an embroidery of a Great Pyrenees dog on the front. There are fixed costs of $580 to set up for production, and variable costs of $39 per jacket. Write
An equation that can be used to determine the total cost, C(x), encountered by Marty's Company in producing x
Jackets.

A) C(x) = (580 + 39) x
B) C(x) = 580x + 39
C) C(x) = 580 - 39x
D) C(x) = 580 + 39x

Question 57

Solve the problem.
In a certain city, the cost of a taxi ride is computed as follows: There is a fixed charge of $2.95 as soon as you get in the taxi, to which a charge of $2.25 per mile is added. Find an equation that can be used to determine the cost, C(x), of an x-mile taxi ride.

A) C(x) = 2.95 + 2.25x
B) C(x) = 3.70x
C) C(x) = 2.25 + 2.95x
D) C(x) = 5.20x

Question 58

Solve the problem.
Northwest Molded molds plastic handles which cost $0.50 per handle to mold. The fixed cost to run the molding machine is $7200 per week. If the company sells the handles for $3.50 each, how many handles must be
Molded and sold weekly to break even?

A) 1800 handles
B) 14,400 handles
C) 1600 handles
D) 2400 handles

Question 59

Solve the problem.
If an object is dropped off of a tower, the velocity, V, of the object after t seconds can be obtained by multiplying t by 32 and adding 10 to the result. Express V as a linear function of t.

A) V(t) = 42t
B) V(t) = 32 + 10t
C) V(t) = 32t + 10 $$\text { D) } V ( t ) = \frac { t - 10 } { 32 }$$

Question 60

Plot and interpret the appropriate scatter diagram.
The table gives the times spent watching TV and the grades of several students. $$\begin{array} { l | c c c c c c } \text { Weekly TV (h) } & 6 & 12 & 18 & 24 & 30 & 36 \\\hline \text { Grade } ( \% ) & 92.5 & 87.5 & 72.5 & 77.5 & 62.5 & 57.5\end{array}$$ Which scatter diagram describes the data and the relationship, if any? A)


More hours spent watching TV may reduce grades. B)

More hours spent watching TV may reduce grades. C)

More hours spent watching TV may increase grades.
D) none of these

Question 61

Determine if the type of relation is linear, nonlinear, or none.

A) none
B) nonlinear
C) linear

Question 62

Determine if the type of relation is linear, nonlinear, or none.

A) none
B) nonlinear
C) linear

Question 63

Use a graphing utility to find the equation of the line of best fit. Round to two decimal places, if necessary.
$$\begin{array} { c | c c c c } \mathrm { x } & 2 & 4 & 5 & 6 \\\hline \mathrm { y } & 7 & 11 & 13 & 20\end{array}$$

A) y = 2.8x
B) y = 3x + 0.15
C) y = 2.8x + 0.15
D) y = 3x

Question 64

Solve the problem.
The following scatter diagram shows heights (in inches) of children and their ages. $$\text { Height (inches) }$$

Age (years) Based on this data, how old do you think a child is who is about 39 inches tall?

A) 1 year
B) 7 years
C) 3 months
D) 3 years

Question 65

Solve the problem.
Identify the scatter diagram of the relation that appears linear. A)

B)

D)

C)

Question 66

Use a graphing utility to find the equation of the line of best fit. Round to two decimal places, if necessary.
$$\begin{array} { l | l l l l l } \mathrm { x } & 6 & 8 & 20 & 28 & 36 \\\hline \mathrm { y } & 2 & 4 & 13 & 20 & 30\end{array}$$

A) y = 0.95x - 2.79
B) y = 0.90x - 3.79
C) y = 0.85x - 2.79
D) y = 0.80x - 3.79

Question 67

Determine if the type of relation is linear, nonlinear, or none.

A) none
B) linear
C) nonlinear

Question 68

Solve the problem.
The following scatter diagram shows heights (in inches) of children and their ages. $$\text { Height (inches) }$$

Age (years) What is the expected height range for a 2-year old child?

A) 35-45 inches
B) 40-50 inches
C) 25-38 inches
D) 20-30 inches

Question 69

Use a graphing utility to find the equation of the line of best fit. Round to two decimal places, if necessary.
$$\begin{array} { l | c c c c c } \mathrm { x } & 24 & 26 & 28 & 30 & 32 \\\hline \mathrm { y } & 15 & 13 & 20 & 16 & 24\end{array}$$

A) y = 1.05x + 11.8
B) y = 1.05x - 11.8
C) y = 0.95x - 11.8
D) y = 0.95x + 11.8

Question 70

Use a graphing utility to find the equation of the line of best fit. Round to two decimal places, if necessary.
$$\begin{array} { l | l l l l l } \mathrm { x } & 1.2 & 1.4 & 1.6 & 1.8 & 2.0 \\\hline \mathrm { y } & 54 & 53 & 55 & 54 & 56\end{array}$$

A) y = 3x + 50
B) y = 55.3
C) y = 2.5x + 50.4
D) y = 54

Question 71

Use a graphing utility to find the equation of the line of best fit. Round to two decimal places, if necessary.
$$\begin{array} { c | c c c c c c } \mathrm { x } & 1 & 2 & 3 & 4 & 5 & 6 \\\hline \mathrm { y } & 17 & 20 & 19 & 22 & 21 & 24\end{array}$$

A) y = 1.03x + 16.4
B) y = 1.03x + 18.9
C) y = 1.17x + 16.4
D) y = 1.17x + 18.9

Question 72

Use a graphing utility to find the equation of the line of best fit. Round to two decimal places, if necessary.
$$\begin{array} { c | c c c c c } x & 1 & 3 & 5 & 7 & 9 \\\hline y & 143 & 116 & 100 & 98 & 90\end{array}$$

A) y = -6.2x + 140.4
B) y = -6.8x + 150.7
C) y = 6.8x - 150.7
D) y = 6.2x - 140.4

Question 73

Determine if the type of relation is linear, nonlinear, or none.

A) nonlinear
B) linear
C) none

Question 74

Determine if the type of relation is linear, nonlinear, or none.

A) nonlinear
B) linear
C) none

Question 75

Plot and interpret the appropriate scatter diagram.
The one-day temperatures for 12 world cities along with their latitudes are shown in the table below. Make a
scatter diagram for the data. Describe what happens to the one-day temperatures as the latitude increases. $$\begin{array} { c | c | c } \text { City } & \text { Temperature (F) } & \text { Latitude } \\\hline \text { Oslo, Norway } & 30 ^ { \circ } & 59 ^ { \circ } \\\text { Seattle, WA } & 57 ^ { \circ } & 47 ^ { \circ } \\\text { Anchorage, AK } & 40 ^ { \circ } & 61 ^ { \circ } \\\text { Paris, France } & 61 ^ { \circ } & 48 ^ { \circ } \\\text { Vancouver, Canada } & 54 ^ { \circ } & 49 ^ { \circ } \\\text { London, England } & 48 ^ { \circ } & 51 ^ { \circ } \\\text { Tokyo, Japan } & 55 ^ { \circ } & 35 ^ { \circ } \\\text { Cairo, Egypt } & 82 ^ { \circ } & 30 ^ { \circ } \\\text { Mexico City, Mexico } & 84 ^ { \circ } & 19 ^ { \circ } \\\text { Miami, FL } & 81 ^ { \circ } & 25 ^ { \circ } \\\text { New Delhi, India } & 95 ^ { \circ } & 28 ^ { \circ } \\\text { Manila, Philippines } & 93 ^ { \circ } & 14 ^ { \circ }\end{array}$$ Latitude (degrees) Temperature (F)°

Question 76

Determine if the type of relation is linear, nonlinear, or none.

A) linear
B) nonlinear
C) none

Question 77

Solve the problem.
The following scatter diagram shows heights (in inches) of children and their ages. Age (years) What happens to height as age increases?

A) Height stays the same as age increases.
B) Height increases as age increases.
C) Height decreases as age increases.
D) Height and age do not appear to be related.

Question 78

Use a graphing utility to find the equation of the line of best fit. Round to two decimal places, if necessary.
$$\begin{array} { c | c c c c c } x & 3 & 5 & 7 & 15 & 16 \\\hline y & 8 & 11 & 7 & 14 & 20\end{array}$$

A) y = 0.75x + 4.07
B) y = 0.85x + 3.07
C) y = 0.95x + 3.07
D) y = 0.75x + 5.07

Question 79

Use a graphing utility to find the equation of the line of best fit. Round to two decimal places, if necessary.
$$\begin{array} { l | l l l l l } \mathrm { x } & 0 & 3 & 4 & 5 & 12 \\\hline \mathrm { y } & 8 & 2 & 6 & 9 & 12\end{array}$$

A) y = 0.53x + 4.88
B) y = 0.73x + 4.98
C) y = 0.63x + 4.88
D) y = 0.43x + 4.98

Question 80

Use a graphing utility to find the equation of the line of best fit. Round to two decimal places, if necessary.
$$\begin{array} { c | c c c c c } \mathrm { x } & 2 & 4 & 6 & 8 & 10 \\\hline \mathrm { y } & 15 & 37 & 60 & 75 & 94\end{array}$$

A) y = 10x - 3
B) y = 9.8x - 2.6
C) y = 9.2x - 2.1
D) y = 9x - 3