Deck 11: Quadratic Functions and Models

Question 1

Select the graph of the quadratic function $f ( x ) = x ^ { 2 } - 3$ .Identify the vertex and axis of symmetry. ?

A)? ?
Vertex: (0,-3)
Axis of symmetry: y-axis
?
B)? ?
?
Vertex: (0,-5)
Axis of symmetry: y-axis
C) ?
?
Vertex: (0,-2)
Axis of symmetry: y-axis
D)? ?
?
Vertex: (0,-1)
Axis of symmetry: y-axis
E)? ?
?
Vertex: (0,-4)
Axis of symmetry: y-axis

Answer 1

? ?
Vertex: (0,-3)
Axis of symmetry: y-axis
?

Question 2

The height y (in feet)of a punted football is given by? $y = - \frac { 20 } { 2025 } x ^ { 2 } + \frac { 9 } { 5 } x + 1.6$ ? where x is the horizontal distance (in feet)from the point at which the ball is punted.
What is the maximum height of the punt? (Round your answer to two decimal places. )
?

A)123.61
B)113.61
C)103.61
D)83.61
E)93.61

Answer 2

83.61

Question 3

Select the graph of the function $y = ( 3 x ) ^ { 2 } - 5$ .Compare the graph of this function with the graph of $y = x ^ { 2 }$ . ?

A) ?
?
Horizontal shrink and vertical shift.
B) ?
?
Horizontal shrink and vertical shift.
C) ?
?
Horizontal shrink and vertical shift.
D) ?
?
Horizontal shrink and vertical shift.
E)? ?
?
Horizontal shrink and vertical shift.

Answer 3

?
?
Horizontal shrink and vertical shift.

Question 4

Select the graph of the function $y = x ^ { 2 } - 1$ .Compare the graph of this function with the graph of $y = x ^ { 2 }$ . ?

A) Vertical shift.
B) Vertical shift.
C) Vertical shift.
D) Vertical shift.
E)? Vertical shift.

Question 5

Select the graph of the quadratic function $f ( x ) = x ^ { 2 } + 2 x + 2$ .Identify the axis of symmetry. ?

A) Axis of symmetry: x = -1
B) ?Axis of symmetry: x = -1
C) Axis of symmetry: x = -1
D) ?Axis of symmetry: x = -1
E) Axis of symmetry: x = -1

Question 6

Select the graph of the function $y = ( x - 4 ) ^ { 2 } + 1$ .Compare the graph of this function with the graph of $y = x ^ { 2 }$ . ?

A) ?
Horizontal shift of 2 units to the right and vertical shift of 1 unit upward.
B) ?
Horizontal shift of 1 units to the right and vertical shift of 1 unit upward.
C) ?
Horizontal shift of 4 units to the right and vertical shift of 1 unit upward.
D)? ?
Horizontal shift of 4 units to the right and vertical shift of 1 unit upward.
E)? ?
Horizontal shift of 3 units to the right and vertical shift of 1 unit upward.

Question 7

Select the graph of the function $y = ( x / 3 ) ^ { 2 } - 3$ .Compare the graph of this function with the graph of $y = x ^ { 2 }$ . ?

A) ?
?
Horizontal stretch and vertical shift.
B)? ?
?
Horizontal stretch and vertical shift.
C) ?
?
Horizontal stretch and vertical shift.
D) ?
?
Horizontal stretch and vertical shift.
E)? ?
?
Horizontal stretch and vertical shift.

Question 8

Find two positive real numbers whose product is a maximum.The sum is 140. ​

A)90,50
B)​100,40
C)​70,​70
D)​80,60
E)​10,130

Question 9

Find two positive real numbers whose product is a maximum. ​
The sum of the first and twice the second is 56.
(Round your answer to two decimal places. )
​

A)28,5.6
B)28,9.33​
C)28,7
D)28,14
E)14,14

Question 10

Select the graph of the function $y = - 6 x ^ { 2 }$ .Compare the graph of this function with the graph of $y = x ^ { 2 }$ . ?

A) ?
Vertical stretch
B) ?
Vertical stretch and reflection in x-axis
C) ?
?
Reflection in x-axis
D) ?
?
Vertical shrink and reflection in x-axis
E) ?
?
Vertical shrink

Question 11

Select the graph of the function $y = x ^ { 2 } + 4$ .Compare the graph of this function with the graph of $y = x ^ { 2 }$ . ?

A) ?
?
Vertical shift.
B) ?
?
Vertical shift.
C) ?
?
Vertical shift.
D) ?
?
Vertical shift.
E)? ?
?
Vertical shift.

Question 12

Select the graph of the function $y = ( x - 1 ) ^ { 2 }$ .Compare the graph of this function with the graph of $y = x ^ { 2 }$ . ?

A) Horizontal shift 3 units to the right.
B) Horizontal shift 4 units to the right.
C) Horizontal shift 5 units to the right.
D) Horizontal shift 1 unit to the right.
E) Horizontal shift 2 units to the right.

Question 13

Select the graph of the quadratic function $f ( x ) = 3 - x ^ { 2 }$ .Identify the vertex and axis of symmetry. ?

A) ?
?
Vertex: (0,3)
Axis of symmetry: y-axis
B) ?
?
Vertex: (0,1)
Axis of symmetry: y-axis
C) ?
?
Vertex: (0,5)
Axis of symmetry: y-axis
D) ?
?
Vertex: (0,4)
Axis of symmetry: y-axis
E)? ?
?
Vertex: (0,2)
Axis of symmetry: y-axis

Question 14

A manufacturer of lighting fixtures has daily production costs of $C = 800 - 80 x + 0.25 x ^ { 2 }$ where C is the total cost (in dollars)and x is the number of units produced.How many fixtures should be produced each day to yield a minimum cost? (Round your answer to two decimal places. )
?

A)160
B)106.67
C)320
D)400
E)800 ?

Question 15

Select the graph of the quadratic function $f ( x ) = ( x + 4 ) ^ { 2 } + 3$ .Identify the vertex and axis of symmetry. ?
?

A)? ?
Vertex: (-4,5)
Axis of symmetry: x = -4
B)? ?
Vertex: (-4,1)
Axis of symmetry: x = -4
C)? ?
Vertex: (-4,2)
Axis of symmetry: x = -4
D) ?
Vertex: (-4,4)
Axis of symmetry: x = -4
E)? Vertex: (-4,3)
Axis of symmetry: x = -4

Question 16

Find two positive real numbers whose product is a maximum. ​
The sum of the first and three times the second is 48.
​

A)24,8
B)24,16
C)16,4
D)24,6
E)42,6

Question 17

Select the graph of the quadratic function $f ( x ) = x ^ { 2 } + 5$ .Identify the vertex and axis of symmetry. ?

A)? ?
?
Vertex: (0,1)
Axis of symmetry: y-axis
B) ?
?
Vertex: (0,3)
Axis of symmetry: y-axis
C) ?
?
Vertex: (0,4)
Axis of symmetry: y-axis
D) ?
Vertex: (0,5)
Axis of symmetry: y-axis
?
E)? ?
Vertex: (0,2)
Axis of symmetry: y-axis

Question 18

Select the graph of the function $y = [ 2 ( x - 1 ) ] ^ { 2 } + 1$ .Compare the graph of this function with the graph of $y = x ^ { 2 }$ . ?

A) ?
?
Horizontal shift of 4 units to the right and vertical shift of 1 unit upward and horizontal shrink
B)? ?
?
Horizontal shift of 2 units to the right and vertical shift of 1 unit upward and horizontal shrink
C)? ?
?
Horizontal shift of 5 units to the right and vertical shift of 1 unit upward and horizontal shrink
D) ?
Horizontal shift of 1 units to the right and vertical shift of 1 unit upward and horizontal shrink
E)? ?
?
Horizontal shift of 3 units to the right and vertical shift of 1 unit upward and horizontal shrink

Question 19

Select the graph of the quadratic function.? $f ( x ) = x ^ { 2 } - 5 x$ ?

A)? ?
B) ?
C) ?
D) ?
E)? ?

Question 20

Select the graph of the function $y = \frac { 3 } { 2 } x ^ { 2 }$ .Compare the graph of this function with the graph of $y = x ^ { 2 }$ . ?

A)? Vertical shrink.
B) ?Vertical stretch.
C) ?
?
Vertical stretch and reflection in the x-axis.
D) ?
?
Vertical shrink.
E)? ?
?
Vertical stretch and reflection in the x-axis.

Question 21

A small theater has a seating capacity of 2000.When the ticket price is $20,attendance is 1500.For each $1 decrease in price,attendance increases by 50.The revenue R of the theater as a function of ticket price x is as follows $R ( x ) = - 50 x ^ { 2 } + 2500 x , 10 \leq x \leq 20$ What ticket price will yield a maximum revenue?

A)$55.00 ?
B)$35.00 ?
C)$25.00 ?
D)$45.00 ?
E)$65.00 ?

Question 22

Determine the x-intercept(s)of the quadratic function $f ( x ) = x ^ { 2 } + 8 x + 12$ .

A) $( 2,0 ) , ( 6,0 )$
B) $( 6,0 ) , ( 5,0 )$
C) $( - 2,0 ) , ( - 6,0 )$
D) $( - 6,0 ) , ( - 5,0 )$
E)no x-intercept(s)

Question 23

Compare the graph of $n ( x ) = 7 ( x - 3 ) ^ { 2 } + 6$ with $n ( x ) = x ^ { 2 }$ .

A) $n ( x ) = 7 ( x - 3 ) ^ { 2 } + 6$ shifts left 3 units,shifts downward 6 units,and stretches by a factor of 7.
B) $n ( x ) = 7 ( x - 3 ) ^ { 2 } + 6$ shifts left 3 units,shifts upward 6 units,and stretches by a factor of 7.
C) $n ( x ) = 7 ( x - 3 ) ^ { 2 } + 6$ shifts right 3 units,shifts downward 6 units,and shrinks by a factor of $\frac { 1 } { 7 }$ .
D) $n ( x ) = 7 ( x - 3 ) ^ { 2 } + 6$ shifts right 3 units,shifts upward 6 units,and shrinks by a factor of $\frac { 1 } { 7 }$ .
E) $n ( x ) = 7 ( x - 3 ) ^ { 2 } + 6$ shifts right 3 units,shifts upward 6 units,and stretches by a factor of 7.

Question 24

The total revenue R earned (in thousands of dollars)from manufacturing handheld video games is given by? $R ( p ) = - 25 p ^ { 2 } + 1200 p$ ? where p is the price per unit (in dollars).
?
Find the revenue when the price per unit is $20.
?

A)$14,000,300
B)$14,000,200
C)$14,000,400
D)$14,000,000
E)$14,000,100

Question 25

From the graph of the quadratic function $f ( x ) = ( x + 6 ) ^ { 2 } - 1$ ,determine the equation of the axis of symmetry.

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

Question 26

The profit P (in hundreds of dollars)that a company makes depends on the amount x (in hundreds of dollars)the company spends on advertising according to the model? $P = 230 + 30 x - 0.5 x ^ { 2 }$ ? What expenditure for advertising will yield a maximum profit?
?

A)30
B)0.5
C)230
D)15
E)115

Question 27

The total revenue R earned per day (in dollars)from a pet-sitting service is given by? $R ( p ) = - 12 p ^ { 2 } + 150 p$ ? where p is the price charged per pet (in dollars).
?
Find the revenue when the price per pet is $3.
?

A)$372.00
B)$352.00
C)$382.00
D)$362.00
E)$342.00

Question 28

Find the values of b such that the function $f ( x ) = x ^ { 2 } + b x - 25$ has the given minimum value -74. ?

A)±16
B)±22
C)±14
D)±18
E)±20

Question 29

Determine the x-intercept(s)of the quadratic function $$f ( x ) = x ^ { 2 } + 2 x + 2$$ .

A) $( 0,0 ) , ( - 5,0 )$
B) $( - 7,0 ) , ( - 4,0 )$
C)no x-intercept(s)
D) $( - 7,0 ) , ( - 5,0 )$
E) $( - 2,0 ) , ( 2,0 )$

Question 30

Determine the vertex of the graph of the quadratic function $f ( x ) = x ^ { 2 } + 5 x + \frac { 29 } { 4 }$ .

A) $\left( \frac { 5 } { 2 } , \frac { 29 } { 4 } \right)$
B) $\left( \frac { 5 } { 4 } , \frac { 21 } { 4 } \right)$
C) $\left( - \frac { 5 } { 2 } , 1 \right)$ ?
D) $\left( - \frac { 5 } { 2 } , \frac { 27 } { 2 } \right)$
E) $\left( 5 , \frac { 29 } { 4 } \right)$

Question 31

Find the values of b such that the function $f ( x ) = - x ^ { 2 } + b x - 75$ has the given maximum value 94. ?

A)±32
B)±28
C)±26
D)±30
E)±34

Question 32

A small theater has a seating capacity of 2000.When the ticket price is $20,attendance is 1500.For each $1 decrease in price,attendance increases by 125.Write the revenue R of the theater as a function of ticket price x. ?

A) $R ( x ) = 125 x ^ { 2 } + 3000 x , 16 \leq x \leq 20$
B) $R ( x ) = - 125 x ^ { 2 } + 1000 x , 16 \leq x \leq 20$
C) $R ( x ) = - 125 x ^ { 3 } + 500 x , 16 \leq x \leq 20$
D) $R ( x ) = - 125 x ^ { 2 } - 350 x , 16 \leq x \leq 20$
E) $R ( x ) = - 125 x ^ { 2 } + 4000 x , 16 \leq x \leq 20$

Question 33

From the graph of the quadratic function $f ( x ) = - x ^ { 2 } + 12 x + 4$ ,determine the equation of the axis of symmetry.

A) $x = 6$
B) $x = 4$
C) $x = 40$
D) $x = - 12$
E) $x = - 32$

Question 34

Find the values of b such that the function $f ( x ) = x ^ { 2 } + b x + 59$ has the given minimum value 10. ?

A)±18
B)±22
C)±14
D)±20
E)±16

Question 35

Compare the graph of $n = \left[ - \frac { 1 } { 9 } ( x + 6 ) \right] ^ { 2 } - 1$ with $n ( x ) = x ^ { 2 }$ .

A) $n = \left[ - \frac { 1 } { 9 } ( x + 6 ) \right] ^ { 2 } - 1$ shifts left 6 units,shifts downward 1 units,and shrinks by a factor of $\frac { 1 } { 81 }$ .
B) $n = \left[ - \frac { 1 } { 9 } ( x + 6 ) \right] ^ { 2 } - 1$ shifts right 6 units,shifts upward 1 units,and shrinks by a factor of $\frac { 1 } { 81 }$ .?
C) $n = \left[ - \frac { 1 } { 9 } ( x + 6 ) \right] ^ { 2 } - 1$ shifts left 36 units,shifts upward 1 units,and shrinks by a factor of $- \frac { 1 } { 9 }$ .
D) $n = \left[ - \frac { 1 } { 9 } ( x + 6 ) \right] ^ { 2 } - 1$ shifts right 36 units,shifts upward 1 units,and shrinks by a factor of $\frac { 1 } { 81 }$ .
E) $n = \left[ - \frac { 1 } { 9 } ( x + 6 ) \right] ^ { 2 } - 1$ shifts right 6 units,shifts downward 1 units,and shrinks by a factor of $- \frac { 1 } { 81 }$ .

Question 36

The total revenue R earned per day (in dollars)from a pet-sitting service is given by? $R ( p ) = - 10 p ^ { 2 } + 120 p$ ? where p is the price charged per pet (in dollars).
?
Find the price that will yield a maximum revenue.
?

A)$7.00
B)$10.00
C)$8.00
D)$6.00
E)$9.00

Question 37

Write the quadratic function $f ( x ) = x ^ { 2 } + 2 x + 5$ in standard form.

A) $$f ( x ) = - ( x + 1 ) ^ { 2 } - 4$$
B) $$f ( x ) = ( x - 4 ) ^ { 2 } - 1$$
C) $f ( x ) = - ( x - 1 ) ^ { 2 } - 4$
D) $f ( x ) = ( x + 1 ) ^ { 2 } + 4$
E) $f ( x ) = - ( x - 4 ) ^ { 2 } + 1$

Question 38

Find the standard form of the quadratic function shown below:? ?

A) $f ( x ) = ( x + 2 ) ^ { 2 } - 3$
B) $f ( x ) =$ $\frac { 1 } { 2 }$ $( x - 2 ) ^ { 2 } + 3$
C) $f ( x ) = -$ $\frac { 2 } { 3 }$ $( x - 1 ) ^ { 2 } + 3$
D) $f ( x ) =$ $\frac { 1 } { 2 }$ $( x + 2 ) ^ { 2 } - 3$
E) $f ( x ) =$ $\frac { 1 } { 4 }$ $( x - 2 ) ^ { 2 } + 3$

Question 39

Find the values of b such that the function $f ( x ) = - x ^ { 2 } + b x - 16$ has the given maximum value 65. ?

A)±18
B)±22
C)±24
D)±20
E)±26

Question 40

The total revenue R earned (in thousands of dollars)from manufacturing handheld video games is given by? $R ( p ) = - 25 p ^ { 2 } + 1900 p$ ? where p is the price per unit (in dollars).
?
Find the unit price that will yield a maximum revenue.
?

A)$42.00
B)$40.00
C)$41.00
D)$39.00
E)$38.00

Question 41

?Write the standard form of the equation of the parabola that has a vertex at (-6,-5)and passes through the point (-8,6). ?

A)? $f ( x ) = \frac { 11 } { 36 } ( x - 6 ) ^ { 2 } - 5$
B)? $f ( x ) = - \frac { 5 } { 36 } ( x + 5 ) ^ { 2 } + 8$
C)? $f ( x ) = \frac { 11 } { 4 } ( x + 6 ) ^ { 2 } - 5$
D)? $f ( x ) = \frac { 3 } { 2 } ( x + 6 ) ^ { 2 } - 8$
E)? $f ( x ) = \frac { 5 } { 8 } ( x + 5 ) ^ { 2 } + 6$

Question 42

A farmer has 216 feet of fencing and wants to build two identical pens for his prize-winning pigs.The pens will be arranged as shown.Determine the dimensions of a pen that will maximize its area.

A) $$7 ^ { \prime} \times 176^ { \prime}$$
B) $$21 ^ { \prime } \times 52 ^ { \prime}$$
C) $27 ^ { \prime} \times 72 ^ { \prime}$
D) $9^ { \prime} \times 108^ { \prime}$
E) $27 ^ { \prime} \times 36 ^ { \prime}$

Question 43

A Norman window has the shape of a rectangle surmounted by a semicircle as in the figure below.If the perimeter of the window is 40 ft,express the area,A,as a function of the width,x,of the window.

A) $$A ( x ) = \frac { 160 x - 4 x ^ { 2 } - \pi x ^ { 2 } } { 8 }$$
B) $$A ( x ) = \frac { 80 x - x ^ { 2 } } { 2 }$$
C) $A ( x ) = \frac { 80 x - 2 x ^ { 2 } - \pi x ^ { 2 } } { 4 }$
D) $A ( x ) = \frac { 80 x + ( 2 - \pi ) x ^ { 2 } } { 4 }$
E) $A ( x ) = \frac { 160 x - 4 x ^ { 2 } - \pi x ^ { 2 } } { 2 }$

Question 44

Write the quadratic function $f ( x ) = \frac { 1 } { 4 } \left( x ^ { 2 } + 8 x - 20 \right)$ in standard form.

A) $f ( x ) = \frac { 1 } { 4 } ( x + 4 ) ^ { 2 } - 9$
B) $f ( x ) = \frac { 1 } { 4 } ( x - 9 ) ^ { 2 } + 4$
C) $f ( x ) = \frac { 1 } { 4 } ( x - 4 ) ^ { 2 } + 9$
D) $f ( x ) = - \frac { 1 } { 9 } ( x + 4 ) ^ { 2 } - 9$
E) $f ( x ) = - \frac { 1 } { 9 } ( x - 4 ) ^ { 2 } - 9$

Question 45

Find the vertex of the parabola. y = x² - 12x + 36

A)(6,0)
B)(0,6)
C)(-24,0)
D)(36,0)
E)(6,-24)

Question 46

Graph the given function.? $f ( x ) = 2 -$ $x ^ { 2 }$ ?

A) ?
B) ?
C) ?
D) ?
E) ?

Question 47

Graph the quadratic function. ​
F (x)= x² + 2x
​

A) ​
B) ​
C) ​
D) ​

Question 48

Find two positive real numbers whose product is a maximum and whose sum is 160.

A) $89,71$
B) $85,75$
C) $80,80$
D) $78,82$
E) $92,68$

Question 49

Find the vertex of the parabola. ​
Y = 3x² - 1
​

A)(-1,3)
B)(0,-1)
C)(3,-1)
D)(-1,0)
E)(0,3)

Question 50

Write the standard form of the equation of the parabola that has a vertex at $\left( - \frac { 2 } { 3 } , \frac { 1 } { 9 } \right)$ and passes through the point $( 2,3 )$ .

A) $f ( x ) = \frac { 13 } { 32 } \left( x - \frac { 3 } { 2 } \right) ^ { 2 } + \frac { 1 } { 9 }$
B) $f ( x ) = \frac { 13 } { 32 } \left( x + \frac { 2 } { 3 } \right) ^ { 2 } + \frac { 1 } { 9 }$
C) $f ( x ) = \frac { 13 } { 4 } \left( x - \frac { 2 } { 3 } \right) ^ { 2 } - \frac { 1 } { 9 }$
D) $f ( x ) = \frac { 13 } { 8 } \left( x - \frac { 3 } { 2 } \right) ^ { 2 } - \frac { 1 } { 9 }$
E) $f ( x ) = \frac { 13 } { 4 } \left( x + \frac { 2 } { 3 } \right) ^ { 2 } + \frac { 1 } { 9 }$

Question 51

The function $f ( x ) = x ^ { 2 } - 5$ is one-to-one on the domain $$( x \leq 0 )$$ .Find $f ^ { - 1 } ( x )$ . ?

A) $f ^ { - 1 } ( x ) = x ^ { 2 } + 5$
B) $f ^ { - 1 } ( x ) = \sqrt { x + 5 }$
C) $f ^ { - 1 } ( x ) = - \sqrt { x + 5 }$
D) $f ^ { - 1 } ( x ) = \frac { 1 } { x ^ { 2 } - 5 }$
E) $f ^ { - 1 } ( x ) = \sqrt { x - 5 }$

Question 52

Graph the quadratic function.? $$f ( x ) = - \frac { 1 } { 3 } x ^ { 2 } - 2$$ ?

A) ?
B) ?
C) ?
D) ?

Question 53

Find the vertex of the parabola.
​
y = x² + 14x + 49
​
Please enter your ANS. as an ordered pair.

Question 54

The height,h(x),of a punted rugby ball is given by $h ( x ) = - \frac { 1 } { 64 } x ^ { 2 } + \frac { 21 } { 32 } x + 3$ where x is the horizontal distance in feet from the point where the ball is punted.How far,horizontally,is the ball from the kicker when it is at its highest point?

A) $45 \text { feet }$
B) $21 \text { feet }$
C) $26 \text { feet }$
D) $31 \text { feet }$
E) $24 \text { feet }$

Question 55

Find two positive real numbers whose product is a maximum and whose sum of the first number and four times the second is 160.

A) $128,8$
B) $88,18$
C) $80,20$
D) $96,16$
E) $56,26$

Question 56

Find the vertex of the parabolic graph of the equation. y = 4(x - 5)² + 7

A)(5,0)
B)(25,7)
C)(5,4)
D)(7,5)
E)(5,7)

Question 57

Graph the quadratic function. ​
F (x)= - 4x² + 2
​

A) ​
B) ​
C) ​
D) ​

Question 58

Find the vertex of the parabola. y = - x² + 16x - 60

A)(-8,4)
B)(8,4)
C)(-8,-4)
D)(8,-30)
E)(4,8)

Question 59

Write the quadratic function $f ( x ) = - x ^ { 2 } + 8 x - 8$ in standard form.

A) $f ( x ) = ( x - 8 ) ^ { 2 } - 4$
B) $f ( x ) = ( x - 4 ) ^ { 2 } - 8$
C) $f ( x ) = - ( x + 4 ) ^ { 2 } + 8$
D) $f ( x ) = - ( x + 8 ) ^ { 2 } - 4$
E) $f ( x ) = - ( x - 4 ) ^ { 2 } + 8$

Question 60

Graph the quadratic function. ​
F (x)= - x² - 4x + 1
​

A) ​
B) ​
C) ​
D) ​

Question 61

Find the inverse of the one-to-one function.? $y = 7 x + 5$ ?

A) $y = \frac { x - 7 } { 5 }$
B) $y = \frac { x - 5 } { 7 }$
C) $y = \frac { 7 } { x - 5 }$
D) $y = \frac { x + 5 } { 7 }$
E)none of the above