Question 1

Find and simplify the difference quotient $$\frac { f ( x + h ) - f ( x ) } { h } , h \neq 0$$ for the given function.
-$$f ( x ) = \frac { 1 } { 5 x }$$

Accepted Answer

A)  $\frac { 1 } { 5 x }$ 
B)  0 
C)  $\frac { - 1 } { x ( x + h ) }$ 
D)  $\frac { - 1 } { 5 x ( x + h ) }$ 
A)  $\frac { 1 } { 5 x }$ 
B)  0 
C)  $\frac { - 1 } { x ( x + h ) }$ 
D)  $\frac { - 1 } { 5 x ( x + h ) }$

Question 2

Use the graph to determine the function's domain and range.
-

Accepted Answer

A)  domain: $( - \infty , \infty )$
range: $[ 2 , \infty )$ 
B)  domain: $[ 0 , \infty )$
range: $( - \infty , \infty )$ 
C)  domain: $[ 0 , \infty )$
 range: $[ 0 , \infty )$ 
D)  domain: $[ 0 , \infty )$   
range: $[ 2 , \infty )$ 
A)  domain: $( - \infty , \infty )$
range: $[ 2 , \infty )$ 
B)  domain: $[ 0 , \infty )$
range: $( - \infty , \infty )$ 
C)  domain: $[ 0 , \infty )$
 range: $[ 0 , \infty )$ 
D)  domain: $[ 0 , \infty )$   
range: $[ 2 , \infty )$

Question 3

Determine whether the relation is a function.
-{(3, -9), (3, 3), (4, 9), (7, 4), (10, 7)}

Accepted Answer

A) Not a function 
B) Function 
A) Not a function 
B) Function

Question 4

Determine whether the given function is even, odd, or neither.
-$$f ( x ) = 2 x ^ { 2 } + x ^ { 4 }$$

Accepted Answer

A)  Even 
B)  Neither 
C)  Odd 
A)  Even 
B)  Neither 
C)  Odd

Question 5

Graph the given functions on the same rectangular coordinate system. Describe how the graph of g is related to the graph
of f.
-$(x)=x, g(x)=x+4$

Accepted Answer

A)  g shifts the graph of f vertically down 4 units
  
B)  g shifts the graph of } f 	ext { vertically down } 4 	ext { units }\)
  
C)  g shifts the graph of f vertically up 4 units
  
D)  g shifts the graph of f vertically up 4 units
  
A)  g shifts the graph of f vertically down 4 units
  
B)  g shifts the graph of } f 	ext { vertically down } 4 	ext { units }\)
  
C)  g shifts the graph of f vertically up 4 units
  
D)  g shifts the graph of f vertically up 4 units

Question 6

Use the given conditions to write an equation for the line in slope-intercept form.
-Passing through $( - 8 , - 3 )$ and $( - 4 , - 8 )$

Accepted Answer

A)  $y = m x - 13$ 
B)  $y = \frac { 5 } { 4 } x - 13$ 
C)  $y + 3 = - \frac { 5 } { 4 } ( x + 8 )$ 
D)  $y = - \frac { 5 } { 4 } x - 13$ 
A)  $y = m x - 13$ 
B)  $y = \frac { 5 } { 4 } x - 13$ 
C)  $y + 3 = - \frac { 5 } { 4 } ( x + 8 )$ 
D)  $y = - \frac { 5 } { 4 } x - 13$

Question 7

Use the graph to find the indicated function value.
-y = f(x). Find f(5)

Accepted Answer

A) -11 
B) 9 
C) 11 
D) 2 
A) -11 
B) 9 
C) 11 
D) 2

Question 8

Determine whether the given function is even, odd, or neither.
-$$f ( x ) = x ^ { 3 } + x ^ { 2 } + 3$$

Accepted Answer

A)  Even 
B)  Neither 
C)  Odd 
A)  Even 
B)  Neither 
C)  Odd

Question 9

Find the slope of the line that goes through the given points.
-(5, -7), (-8, -2)

Accepted Answer

A)  $- \frac { 5 } { 13 }$ 
B)  $- \frac { 13 } { 5 }$ 
C)  $- 2$ 
D)  $- \frac { 1 } { 2 }$ 
A)  $- \frac { 5 } { 13 }$ 
B)  $- \frac { 13 } { 5 }$ 
C)  $- 2$ 
D)  $- \frac { 1 } { 2 }$

Question 10

Solve the problem.
-The function $\mathrm { P } ( \mathrm { x } ) = 0.35 \mathrm { x } - 74$ models the relationship between the number of pretzels $x$ that a certain vendor sells and the profit the vendor makes. Find $\mathrm { P } ( 1000 )$, the profit the vendor makes from selling 1000 pretzels.

Accepted Answer

A)  $\$ 926$ 
B)  $\$ 424$ 
C)  $\$ 350$ 
D)  $\$ 276$ 
A)  $\$ 926$ 
B)  $\$ 424$ 
C)  $\$ 350$ 
D)  $\$ 276$

Question 11

Use the given conditions to write an equation for the line in point-slope form.
-Slope $= 3$, passing through $( 5,8 )$

Accepted Answer

A)  $x - 8 = 3 ( y - 5 )$ 
B)  $y + 8 = 3 ( x + 5 )$ 
C)  $y - 8 = 3 ( x - 5 )$ 
D)  $y = 3 x - 7$ 
A)  $x - 8 = 3 ( y - 5 )$ 
B)  $y + 8 = 3 ( x + 5 )$ 
C)  $y - 8 = 3 ( x - 5 )$ 
D)  $y = 3 x - 7$

Question 12

Use the given conditions to write an equation for the line in slope-intercept form.
-Slope $= \frac { 4 } { 7 } , \mathrm { y }$-intercept $= 2$

Accepted Answer

A)  $f ( x ) = \frac { 7 } { 4 } x + \frac { 7 } { 2 }$ 
B)  $f ( x ) = \frac { 4 } { 7 } x - 2$ 
C)  $f ( x ) = \frac { 4 } { 7 } x + 2$ 
D)  $f ( x ) = - \frac { 4 } { 7 } x - 2$ 
A)  $f ( x ) = \frac { 7 } { 4 } x + \frac { 7 } { 2 }$ 
B)  $f ( x ) = \frac { 4 } { 7 } x - 2$ 
C)  $f ( x ) = \frac { 4 } { 7 } x + 2$ 
D)  $f ( x ) = - \frac { 4 } { 7 } x - 2$

Question 13

Use the graph to find the indicated function value.
-y = f(x). Find f(-4)

Accepted Answer

A) 4 
B) 0 
C) 3 
D) 9 
A) 4 
B) 0 
C) 3 
D) 9

Question 14

Determine whether the equation defines y as a function of x.
-$$y = - \sqrt { x - 9 }$$

Accepted Answer

A)  $y$ is a function of $x$ 
B)  $y$ is not a function of $x$ 
A)  $y$ is a function of $x$ 
B)  $y$ is not a function of $x$

Question 15

Identify the intercepts
-

Accepted Answer

A)  $( - 3,0 ) , ( 0,6 )$ 
B)  $( 3,0 ) , ( 0,6 )$ 
C)  $( 3,0 ) , ( 0 , - 6 )$ 
D)  $( - 6,0 ) , ( 0,6 )$ 
A)  $( - 3,0 ) , ( 0,6 )$ 
B)  $( 3,0 ) , ( 0,6 )$ 
C)  $( 3,0 ) , ( 0 , - 6 )$ 
D)  $( - 6,0 ) , ( 0,6 )$

Question 16

Identify the intervals where the function is changing as requested.
-Increasing

Accepted Answer

A)  $( - 2 , - 1 )$ or $( 3 , \infty )$ 
B)  $( - 1 , \infty )$ 
C)  $( - 1,3 )$ 
D)  $( - 2,1 )$ 
A)  $( - 2 , - 1 )$ or $( 3 , \infty )$ 
B)  $( - 1 , \infty )$ 
C)  $( - 1,3 )$ 
D)  $( - 2,1 )$

Question 17

Use the given conditions to write an equation for the line in slope-intercept form.
-Passing through $( 5,3 )$ and $( 4,6 )$

Accepted Answer

A)  $y = m x + 18$ 
B)  $y = 3 x + 18$ 
C)  $y - 3 = - 3 ( x - 5 )$ 
D)  $y = - 3 x + 18$ 
A)  $y = m x + 18$ 
B)  $y = 3 x + 18$ 
C)  $y - 3 = - 3 ( x - 5 )$ 
D)  $y = - 3 x + 18$

Question 18

Use possible symmetry to determine whether the graph is the graph of an even function, an odd function, or a function
that is neither even nor odd.
-

Accepted Answer

A) Odd 
B) Even 
C) Neither 
A) Odd 
B) Even 
C) Neither

Question 19

Use the vertical line test to determine whether or not the graph is a graph in which y is a function of x.
-

Accepted Answer

A) not a function 
B) function 
A) not a function 
B) function

Question 20

Determine whether the relation is a function.
-{(-7, 2), (-3, -3), (1, 8), (2, 3)}

Accepted Answer

A) Not a function 
B) Function 
A) Not a function 
B) Function

Find and simplify the difference quotient $\frac { f ( x + h ) - f ( x ) } { h } , h \neq 0$ for the given function. - $f ( x ) = \frac { 1 } { 5 x }$

Use the graph to determine the function's domain and range. -

Determine whether the relation is a function. -{(3, -9), (3, 3), (4, 9), (7, 4), (10, 7)}

Determine whether the given function is even, odd, or neither. - $f ( x ) = 2 x ^ { 2 } + x ^ { 4 }$

Graph the given functions on the same rectangular coordinate system. Describe how the graph of g is related to the graph of f. - $(x)=x, g(x)=x+4$

Use the given conditions to write an equation for the line in slope-intercept form. -Passing through $( - 8 , - 3 )$ and $( - 4 , - 8 )$

Use the graph to find the indicated function value. -y = f(x). Find f(5)

Determine whether the given function is even, odd, or neither. - $f ( x ) = x ^ { 3 } + x ^ { 2 } + 3$

Find the slope of the line that goes through the given points. -(5, -7), (-8, -2)

Solve the problem. -The function $\mathrm { P } ( \mathrm { x } ) = 0.35 \mathrm { x } - 74$ models the relationship between the number of pretzels $x$ that a certain vendor sells and the profit the vendor makes. Find $\mathrm { P } ( 1000 )$ , the profit the vendor makes from selling 1000 pretzels.

Use the given conditions to write an equation for the line in point-slope form. -Slope $= 3$ , passing through $( 5,8 )$

Use the given conditions to write an equation for the line in slope-intercept form. -Slope $= \frac { 4 } { 7 } , \mathrm { y }$ -intercept $= 2$

Use the graph to find the indicated function value. -y = f(x). Find f(-4)

Determine whether the equation defines y as a function of x. - $y = - \sqrt { x - 9 }$

Identify the intercepts -

Identify the intervals where the function is changing as requested. -Increasing

Use the given conditions to write an equation for the line in slope-intercept form. -Passing through $( 5,3 )$ and $( 4,6 )$

Use possible symmetry to determine whether the graph is the graph of an even function, an odd function, or a function that is neither even nor odd. -

Use the vertical line test to determine whether or not the graph is a graph in which y is a function of x. -

Determine whether the relation is a function. -{(-7, 2), (-3, -3), (1, 8), (2, 3)}

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Exam 2: Functions and Graphs

Find and simplify the difference quotient f(x+h)−f(x)h,h≠0\frac { f ( x + h ) - f ( x ) } { h } , h \neq 0hf(x+h)−f(x)​,h=0 for the given function. - f(x)=15xf ( x ) = \frac { 1 } { 5 x }f(x)=5x1​