Deck 2: Linear and Quadratic Functions

Question 1

Determine the slope and y-intercept of the function.
F(x) = 1

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

Answer 1

D

Question 2

Determine the slope and y-intercept of the function.

- $$G ( x ) = - 5 x$$

A) $m = 5 ; b = 0$
B) $m = 0 ; b = - 5$
C) $\mathrm { m } = - 5 ; \mathrm { b } = 0$
D) $\mathrm { m } = - \frac { 1 } { 5 } ; \mathrm { b } = 0$

Answer 2

$\mathrm { m } = - 5 ; \mathrm { b } = 0$

Question 3

Determine the slope and y-intercept of the function.
h(x) = -2x - 6

A) m = 2; b = 6
B) m = 2; b = - 6
C) m = -2; b = - 6
D) m = -2; b = 6

Answer 3

C

Question 4

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

- $f(x)=2 x-2$

A)

B)

C)

D)

Question 5

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

Question 6

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

- $F(x)=2$

A)

B)

C)

D)

Question 7

Determine the average rate of change for the function.
h(x) = -4x + 10

A) 10
B) -10
C) -4
D) 4

Question 8

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

- $p(x)=-x-4$

A)

B)

C)

D)

Question 9

Determine the slope and y-intercept of the function.

- $$f ( x ) = \frac { 1 } { 4 } x - 3$$

A) $\mathrm { m } = - \frac { 1 } { 4 } ; \mathrm { b } = 3$
B) $\mathrm { m } = 4 ; \mathrm { b } = 3$
C) $\mathrm { m } = \frac { 1 } { 4 } ; \mathrm { b } = - 3$
D) $m = - 3 ; b = \frac { 1 } { 4 }$

Question 10

Determine whether the given function is linear or nonlinear.

- $$\begin{array} { c | c } x & y = f ( x ) \\\hline 3 & 12 \\5 & 20 \\7 & 28 \\9 & 36\end{array}$$

A) nonlinear
B) linear

Question 11

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

- $g(x)=-2 x+1$

A)

B)

C)

D)

Question 12

Determine the average rate of change for the function.

- $$F ( x ) = - 5$$

A) $- \frac { 1 } { 5 }$
B) 5
C) 0
D) $- 5$

Question 13

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

- $$G ( x ) = - 3 x$$

A)

B)

C)

D)

Question 14

Determine the slope and y-intercept of the function.
f(x) = 2x + 11

A) m = 2; b = -11
B) m = -2; b = 11
C) m = -2; b = -11
D) m = 2; b = 11

Question 15

Determine the slope and y-intercept of the function.
p(x) = -x - 3

A) m =1; b = 3
B) m = -1; b = 3
C) m = 0; b = -3
D) m = -1; b =-3

Question 16

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

- $$f ( x ) = \frac { 1 } { 2 } x - 3$$

A)

B)

C)

D)

Question 17

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

- $$\mathrm { F } ( \mathrm { x } ) = \frac { 1 } { 6 } \mathrm { x }$$

A)

B)

C)

D)

Question 18

Determine the average rate of change for the function.
p(x) = -x + 1

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

Question 19

Determine the average rate of change for the function.
f(x) = 5x - 3

A) 3
B) -5
C) - 3
D) 5

Question 20

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

- $$h ( x ) = - \frac { 3 } { 4 } x + 3$$

A)

B)

C)

D)

Question 21

Find the zero of the linear function.

- $$F ( x ) = \frac { 1 } { 7 } x - 9$$

A) 63
B) $\frac { 9 } { 7 }$
C) $- 63$
D) $- \frac { 9 } { 7 }$

Question 22

Find the zero of the linear function.
g(x) = 6x - 36

A) -36
B) 0
C) 6
D) -6

Question 23

Find the zero of the linear function.
f(x) = x + 7

A) 7
B) -7
C) 0
D) 14

Question 24

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

- $F(x)=6$

A) constant

B) constant

C) decreasing

D) constant

Question 25

Find the zero of the linear function.

- $$h ( x ) = - 2 x + 3$$

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

Question 26

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

- $$f ( x ) = \frac { 1 } { 2 } x - 2$$

A) increasing

B) increasing

C) decreasing

D) increasing

Question 27

Determine the average rate of change for the function.

- $$f ( x ) = \frac { 1 } { 2 } x - 3$$

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

Question 28

Find the zero of the linear function.

- $$G ( x ) = - \frac { 1 } { 4 } x - 4$$

A) $- 16$
B) $- 1$
C) 16
D) 1

Question 29

Determine the average rate of change for the function.

- $$h ( x ) = - \frac { 3 } { 4 } x - 3$$

A) $- \frac { 3 } { 4 }$
B) 3
C) $\frac { 3 } { 4 }$
D) $- 3$

Question 30

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

- $$h ( x ) = - \frac { 2 } { 5 } x + 2$$

A) decreasing

B) decreasing

C) increasing

D) decreasing

Question 31

Find the zero of the linear function.
f(x) = 6x + 42

A) 42
B) 0
C) 7
D) -7

Question 32

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

- $$\begin{array}{l}g ( x ) = 4 x - 6\\\end{array}$$

A) increasing

B) decreasing

C) increasing

D) decreasing

Question 33

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

- $f(x)=2 x+4$

A) decreasing

B) increasing

C) increasing

D) increasing

Question 34

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

- $$h ( x ) = - 2 x + 5$$

A) increasing

B) decreasing

C) decreasing

D) increasing

Question 35

Solve the problem.

-Suppose that $f ( x ) = - x - 6$ and $g ( x ) = x - 11$ .
(a) Solve $f ( x ) = 0$ .
(b) Solve $g ( x ) = 0$ .
(c) Solve $f ( x ) = g ( x )$ .

A) (a) $x = 6$ ; (b) $x = 11$ ; (c) $x = 2.5$

B) $( \mathrm { a } ) \mathrm { x } = - 6$ ;(b) $x = 11$ ;(c) $x = 2.5$

C) (a) $x = - 6$ ;(b) $x = 11$ ;(c) $x = - 8.5$

D) (a) $x = - 6$ ;(b) $x = - 11$ ;(c) $x = 2.5$

Question 36

Solve the problem.

-Suppose that $f ( x ) = - x - 7$ and $g ( x ) = x - 18$ .
(a) Solve $f ( x ) > 0$ .
(b) Solve $g ( x ) > 0$ .
(c) Solve $\mathrm { f } ( \mathrm { x } ) \leq \mathrm { g } ( \mathrm { x } )$ .

A) (a) $x < - 7$ ;(b) $x < - 18$ ; (c) $x \leq 5.5$

B) $( a ) x > 7$ ;(b) $x > 18$ ;(c) $x > 5.5$

C) (a) $x < - 7$ ; (b) $x > 18$ ; (c) $x \geq 5.5$

D) (a) $x < - 7$ ;(b) $x < 18$ ;(c) $x \geq - 12.5$

Question 37

Find the zero of the linear function.
h(x) = 11 - x

A) -22
B) 1
C) 11
D) -11

Question 38

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

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

Question 39

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

- $p(x)=-x+2$

A) increasing

B) decreasing

C) increasing

D) decreasing

Question 40

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

- $$h ( x ) = - 3 x - 4$$

A) decreasing

B) increasing

C) increasing

D) decreasing

Question 41

Solve the problem.
The cost for labor associated with fixing a washing machine is computed as follows: There is a fixed charge of $30 for the repairman to come to the house, to which a charge of $23 per hour is added. Find an equation that can be used to determine the labor cost, C(x), of a repair that takes x hours.

A) C(x) = 30 + 23x B) C(x) = 30 - 23x C) C(x) = ( 30 + 23) x D) C(x) = 23 + 30x

Question 42

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 $650 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, and use the equation to find the total cost of producing 79 jackets.

A) $3,711
B) $3,723
C) $3,731
D) $3,743

Question 43

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(7.4), the velocity of the object at time t = 7.4 seconds.

A) V(7.4) = 244.8 feet per second
B) V(7.4) = 248.1 feet per second
C) V(7.4) = 246.8 feet per second
D) V(7.4) = 246.1 feet per second

Question 44

Plot a scatter diagram.

- $\begin{array}{l|lllllllll}\mathrm{x} & 15 & 21 & 36 & 46 & 58 & 70 & 71 & 84 & 95 \\\hline \mathrm{y} & 10 & 23 & 42 & 45 & 68 & 55 & 63 & 96 & 85\end{array}$

A)


B)


C)


D)

Question 45

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

Question 46

Plot a scatter diagram.

- $$\begin{array} { c | c c c c c c c c c c } x & 24 & - 13 & 7 & - 10 & - 6 & 17 & 6 & 18 & 10 & 1 \\\hline y & 56 & 26 & 41 & - 12 & - 2 & 29 & 7 & 71 & - 9 & 5\end{array}$$

A)


B)


C)


D)

Question 47

Solve the problem.
A lumber yard has fixed costs of $4,726.80 per day and variable costs of $0.1 per board-foot produced. Lumber sells for $1.90 per board-foot. How many board-feet must be produced and sold daily to break even?

A) 2,363 board-feet
B) 47,268 board-feet
C) 1,750 board-feet
D) 2,626 board-feet

Question 48

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 = -3
B) x = -1
C) x = 1
D) x = 3

Question 49

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

Question 50

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 $560 to set up for production, and variable costs of $33 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) = 560x + 33
B) C(x) = 560 + 33x
C) C(x) = (560 + 33) x
D) C(x) = 560 - 33x

Question 51

Solve the problem.
Regrind, Inc. regrinds used typewriter platens. The variable cost per platen is $1.50. The total cost to regrind 90 platens is $400. Find the linear cost function to regrind platens. If reground platens sell for $8.00 each, how
Many must be reground and sold to break even?

A) C(x) = 1.50x + 400; 62 platens
B) C(x) = 1.50x + 265; 28 platens
C) C(x) = 1.50x + 400; 43 platens
D) C(x) = 1.50x + 265; 41 platens

Question 52

Solve the problem.
A truck rental company rents a moving truck one day by charging $39 plus $0.09 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 120 miles?

A) C(x) = 0.09x - 39; -$28.20
B) C(x) = 0.09x + 39; $49.80
C) C(x) = 0.09x + 39; $40.08
D) C(x) = 39x + 0.09; $4,680.09

Question 53

Solve the problem.
Northwest Molded molds plastic handles which cost $0.20 per handle to mold. The fixed cost to run the molding machine is $5,253 per week. If the company sells the handles for $3.20 each, how many handles must
Be molded and sold weekly to break even?

A) 1,167 handles
B) 1,544 handles
C) 26,265 handles
D) 1,751 handles

Question 54

Solve the problem.
In a certain city, the cost of a taxi ride is computed as follows: There is a fixed charge of $2.40 as soon as you get in the taxi, to which a charge of $1.90 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) = 1.90 + 2.40x B) C(x) = 4.30x C) C(x) = 2.80x D) C(x) = 2.40 + 1.90x

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) $$f ( x ) \geq g ( x )$$

A) $x \geq - 1$
B) $x \leq 2$
C) $x < - 1$
D) $x \geq 2$

Question 56

Plot and interpret the appropriate scatter diagram.

-The table gives the times spent watching TV and the grades of several students. $\begin{array}{l|cccccc}\text { Weekly TV (h) } & 6 & 12 & 18 & 24 & 30 & 36 \\\hline \text { Grade (\%) } & 92.5 & 87.5 & 72.5 & 77.5 & 62.5 & 57.5\end{array}$

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 increase grades.

C)

More hours spent watching TV may reduce grades.

D) none of these

Question 57

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.

Question 58

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 59

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) = 5,000 - 100p and D(p) = 150p, where p is the price. Find the equilibrium price for
Caps at the game. Then find the equilibrium quantity.

A) $20, $3,000
B) $33, $1,700
C) $50, $0
D) $50, $3,000

Question 60

Solve the problem.
Linda needs to have her car towed. Little Town Auto charges a flat fee of $75 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 3
Miles.

A) c(x) = 3x + 75; $84
B) c(x) = 3x; $78
C) c(x) = 3x + 75; $74
D) c(x) = 3x; $9

Question 61

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

Question 62

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

A) none
B) nonlinear
C) linear

Question 63

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

Question 64

Use a graphing utility to find the equation of the line of best fit. Round to two decimal places, if necessary.

- $\begin{array}{c|ccccc}\mathrm{x} & 1 & 3 & 5 & 7 & 9 \\\hline \mathrm{y} & 143 & 116 & 100 & 98 & 90\end{array}$

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

Question 65

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

A) linear
B) none
C) nonlinear

Question 66

Use a graphing utility to find the equation of the line of best fit. Round to two decimal places, if necessary.

- $\begin{array}{l|lllll}\mathrm{x} & 0 & 3 & 4 & 5 & 12 \\\hline \mathrm{y} & 8 & 2 & 6 & 9 & 12\end{array}$

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

Question 67

Use a graphing utility to find the equation of the line of best fit. Round to two decimal places, if necessary.

- $\begin{array}{l|lllll}\mathrm{x} & 24 & 26 & 28 & 30 & 32 \\\hline \mathrm{y} & 15 & 13 & 20 & 16 & 24\end{array}$

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

Question 68

Use a graphing utility to find the equation of the line of best fit. Round to two decimal places, if necessary.

- $\begin{array}{l|lllll}\mathrm{x} & 1.2 & 1.4 & 1.6 & 1.8 & 2.0 \\\hline \mathrm{y} & 54 & 53 & 55 & 54 & 56\end{array}$

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

Question 69

Use a graphing utility to find the equation of the line of best fit. Round to two decimal places, if necessary.

- $\begin{array}{c|cccc}\mathrm{x} & 2 & 4 & 5 & 6 \\\hline \mathrm{y} & 7 & 11 & 13 & 20\end{array}$

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

Question 70

Solve the problem.

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

Age (years)
What happens to height as age increases?

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

Question 71

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. Latitude (degrees) Temperature (F)°

Question 72

Use a graphing utility to find the equation of the line of best fit. Round to two decimal places, if necessary.

- $\begin{array}{c|ccccc}\mathrm{x} & 3 & 5 & 7 & 15 & 16 \\\hline \mathrm{y} & 8 & 11 & 7 & 14 & 20\end{array}$

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

Question 73

Use a graphing utility to find the equation of the line of best fit. Round to two decimal places, if necessary.

- $\begin{array}{l|lllll}\mathrm{x} & 6 & 8 & 20 & 28 & 36 \\\hline \mathrm{y} & 2 & 4 & 13 & 20 & 30\end{array}$

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

Question 74

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

A) none
B) linear
C) nonlinear

Question 75

Use a graphing utility to find the equation of the line of best fit. Round to two decimal places, if necessary.

- $\begin{array}{c|ccccc}\mathrm{x} & 2 & 4 & 6 & 8 & 10 \\\hline \mathrm{y} & 15 & 37 & 60 & 75 & 94\end{array}$

A) $y = 9 x - 3$
B) $y = 9.8 x - 2.6$
C) $\mathrm { y } = 9.2 \mathrm { x } - 2.1$
D) $y = 10 x - 3$

Question 76

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

A) none
B) linear
C) nonlinear

Question 77

Use a graphing utility to find the equation of the line of best fit. Round to two decimal places, if necessary.

- $\begin{array}{c|cccccc}\mathrm{x} & 1 & 2 & 3 & 4 & 5 & 6 \\\hline \mathrm{y} & 17 & 20 & 19 & 22 & 21 & 24\end{array}$

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

Question 78

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

A) nonlinear
B) none
C) linear

Question 79

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

A) nonlinear
B) none
C) linear

Question 80

Solve the problem.

-Identify the scatter diagram of the relation that appears linear.

A)


B)


C)


D)