Question 1

Determine $( g \circ f ) ( x )$ for the pair of functions $f ( x ) = 8 x + 3$ and $g ( x ) = x ^ { 2 } + 7$ .

Accepted Answer

A)  $( 8 x + 3 ) ^ { 2 } + 7$ 
B)  $( 8 x ) ^ { 2 } + 7$ 
C)  $8 x + 10$ 
D)  $( 3 x + 8 ) ^ { 2 } - 7$ 
E)  $( 8 x - 3 ) ^ { 2 } - 7$ 
A)  $( 8 x + 3 ) ^ { 2 } + 7$ 
B)  $( 8 x ) ^ { 2 } + 7$ 
C)  $8 x + 10$ 
D)  $( 3 x + 8 ) ^ { 2 } - 7$ 
E)  $( 8 x - 3 ) ^ { 2 } - 7$

Question 2

Find the constant of variation for the stated condition: y varies directly as x , and y = 150 when x = 240.

Accepted Answer

A)  $k = \frac { 5 } { 4 }$ 
B)  $k = \frac { 1 } { 4 }$ 
C)  $k = 14,580$ 
D)  $k = \frac { 4 } { 5 }$ 
E)  $k = \frac { 1 } { 5 }$ 
A)  $k = \frac { 5 } { 4 }$ 
B)  $k = \frac { 1 } { 4 }$ 
C)  $k = 14,580$ 
D)  $k = \frac { 4 } { 5 }$ 
E)  $k = \frac { 1 } { 5 }$

Question 3

Determine $( g \circ f ) ( x )$ for the pair of functions $f ( x ) = 5 x + 4$ and $g ( x ) = 3 x - 7$ .

Accepted Answer

A)  $15 x$ 
B)  $15 x ^ { 2 } + 5$ 
C)  $15 x + 5$ 
D)  $15 x - 5$ 
E)  $15 - 7 x$ 
A)  $15 x$ 
B)  $15 x ^ { 2 } + 5$ 
C)  $15 x + 5$ 
D)  $15 x - 5$ 
E)  $15 - 7 x$

Question 4

Graph the function. $f ( x ) = \frac { 1 } { 6 } | x |$

Accepted Answer

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

Question 5

Find $\frac { f ( a + h ) - f ( a ) } { h }$ for f ( x )= - x 2S1S1P0 - 7.

Accepted Answer

A) h + a 
B) -7 
C) -2 a - h 
D) 7 a 
E) -2 a S1U1P1 2 S1S1P0- h 
A) h + a 
B) -7 
C) -2 a - h 
D) 7 a 
E) -2 a S1U1P1 2 S1S1P0- h

Question 6

If you have the following function, f ( x )= -7| x | + 8, compute f (1), f (-3), f (2), f (-4)

Accepted Answer

A) f (1)= 1, f (-3)= -13, f (2)= -6, f (-4)= -20 
B) f (1)= 2, f (-3)= -14, f (2)= -5, f (-4)= -21 
C) f (1)= 2, f (-3)= -11, f (2)= -7, f (-4)= -18 
D) f (1)= 4, f (-3)= -15, f (2)= -3, f (-4)= -22 
E) f (1)= -1, f (-3)= 13, f (2)= 6, f (-4)= 20 
A) f (1)= 1, f (-3)= -13, f (2)= -6, f (-4)= -20 
B) f (1)= 2, f (-3)= -14, f (2)= -5, f (-4)= -21 
C) f (1)= 2, f (-3)= -11, f (2)= -7, f (-4)= -18 
D) f (1)= 4, f (-3)= -15, f (2)= -3, f (-4)= -22 
E) f (1)= -1, f (-3)= 13, f (2)= 6, f (-4)= 20

Question 7

Form the inverse function of the function and list the range of the inverse function. f = { (1, 8), (2, 9), (4, 11), (3, 7)}

Accepted Answer

A) { 1, 8, 2, 9 } 
B) { 1, 2, 4, 3 } 
C) { 4, 9, 3, 7 } 
D) { 0, 2, 4, 3 } 
E) { 8, 9, 11, 7 } 
A) { 1, 8, 2, 9 } 
B) { 1, 2, 4, 3 } 
C) { 4, 9, 3, 7 } 
D) { 0, 2, 4, 3 } 
E) { 8, 9, 11, 7 }

Question 8

Graph the function $y = \sqrt { x }$ .

Accepted Answer

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

Question 9

Graph the function. Check your work with a graphing calculator. $f ( x ) = | x | + 7$

Accepted Answer

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

Question 10

The volume of a cylinder varies jointly as its altitude and the square of the radius of its base. If the volume of a cylinder is 2,199 cubic centimeters when the radius of the base is 10 centimeters and its altitude is 7 centimeters, find the volume of a cylinder that has a base of radius 70 centimeters. The altitude of the cylinder is 56 centimeters.

Accepted Answer

A) V = 861,952 cm  3 
B) V = 862,023 cm  3 
C) V = 861,979 cm  3 
D) V = 862,008 cm  3 
E) V = 862,118 cm  3 
A) V = 861,952 cm  3 
B) V = 862,023 cm  3 
C) V = 861,979 cm  3 
D) V = 862,008 cm  3 
E) V = 862,118 cm  3

Question 11

True or false? The function below is one-to-one function. f ( x )= - x  8

Accepted Answer

A) True 
 B)False

Question 12

Find $\frac { f ( a + h ) - f ( a ) } { h }$ for f ( x )= x 2S1S1P0 - 8 x + 2.

Accepted Answer

A) 2 a + h 
B) a + h - 2 
C) -2 a - h + 8 
D) 2 a + h - 10 
E) 2 a + h - 8 
A) 2 a + h 
B) a + h - 2 
C) -2 a - h + 8 
D) 2 a + h - 10 
E) 2 a + h - 8

Question 13

Identify the graph of the function. f ( x )= -3 x  2 - 6 x

Accepted Answer

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

Question 14

If you have the following function, f ( x )= - x  2 - 5 x + 4, compute f (3), f (-2), f (5), f (-4).

Accepted Answer

A) f (3)= 0, f (-2)= 21, f (5)= 6, f (-4)= 43 
B) f (3)= -2, f (-2)= 18, f (5)= 4, f (-4)= 40 
C) f (3)= 1, f (-2)= 20, f (5)= 7, f (-4)= 42 
D) f (3)= -1, f (-2)= 19, f (5)= 5, f (-4)= 41 
E) f (3)= -3, f (-2)= 16, f (5)= 2, f (-4)= 39 
A) f (3)= 0, f (-2)= 21, f (5)= 6, f (-4)= 43 
B) f (3)= -2, f (-2)= 18, f (5)= 4, f (-4)= 40 
C) f (3)= 1, f (-2)= 20, f (5)= 7, f (-4)= 42 
D) f (3)= -1, f (-2)= 19, f (5)= 5, f (-4)= 41 
E) f (3)= -3, f (-2)= 16, f (5)= 2, f (-4)= 39

Question 15

The linear depreciation method assumes that an item depreciates the same amount each year. Suppose a new piece of machinery costs $33,000 and it depreciates $850 each year for t years. Set up a linear function that yields the value of the machinery after t years.

Accepted Answer

A) f ( t )= 850 t - 33,000 
B) f ( t )= 850 t + 33,000 
C) f ( t )= 33,000 - 850 t 
D) f ( t )= 33,000 t + 850 
E) f ( t )= 33,000 t - 850 
A) f ( t )= 850 t - 33,000 
B) f ( t )= 850 t + 33,000 
C) f ( t )= 33,000 - 850 t 
D) f ( t )= 33,000 t + 850 
E) f ( t )= 33,000 t - 850

Question 16

Translate the statement of variation into an equation and use k as the constant of variation. A varies jointly as n and t .

Accepted Answer

A) A = knt 
B) n = kAt 
C)  $C = \frac { k t } { m }$ 
D) A = nt 
E)  $C = \frac { k } { m t }$ 
A) A = knt 
B) n = kAt 
C)  $C = \frac { k t } { m }$ 
D) A = nt 
E)  $C = \frac { k } { m t }$

Question 17

Specify the domain of $( g \circ f ) ( x )$ for the pair of functions $f ( x ) = \frac { 7 } { 4 x }$ and $g ( x ) = \frac { 1 } { x + 3 }$ .

Accepted Answer

A)  $( - \infty , - 3 ) \cup ( - 3,0 ) \cup ( 0 , \infty )$ 
B)  $( - \infty , - 3 ) \cup ( - 3 , \infty )$ 
C)  $( - \infty , - 3 ) \cup ( 0 , \infty )$ 
D)  $\left( - \infty , - \frac { 7 } { 12 } \right) \cup \left( - \frac { 7 } { 12 } , 0 \right) \cup ( 0 , \infty )$ 
E)  $( - \infty , 0 ) \cup ( 0 , \infty )$ 
A)  $( - \infty , - 3 ) \cup ( - 3,0 ) \cup ( 0 , \infty )$ 
B)  $( - \infty , - 3 ) \cup ( - 3 , \infty )$ 
C)  $( - \infty , - 3 ) \cup ( 0 , \infty )$ 
D)  $\left( - \infty , - \frac { 7 } { 12 } \right) \cup \left( - \frac { 7 } { 12 } , 0 \right) \cup ( 0 , \infty )$ 
E)  $( - \infty , 0 ) \cup ( 0 , \infty )$

Question 18

Translate the statement of variation into an equation and use k as the constant of variation. d varies directly as the cube of t .

Accepted Answer

A) t = kd  3 
B) d = t  3 
C)  $d = \frac { k } { b ^ { 3 } }$ 
D) d = kt  3 
E) d = kt 
A) t = kd  3 
B) d = t  3 
C)  $d = \frac { k } { b ^ { 3 } }$ 
D) d = kt  3 
E) d = kt

Question 19

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

Accepted Answer

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

Question 20

Specify the domain of $( g \circ f ) ( x )$ for the pair of functions $f ( x ) = 3 x$ and $g ( x ) = 8 x - 7$ .

Accepted Answer

A)  $( - \infty , 0 )$ 
B)  $( - \infty , 0 ) \cup ( 0 , \infty )$ 
C)  $( 0 , \infty )$ 
D)  $( - \infty , \infty )$ 
E)  $( - \infty , 0 ]$ 
A)  $( - \infty , 0 )$ 
B)  $( - \infty , 0 ) \cup ( 0 , \infty )$ 
C)  $( 0 , \infty )$ 
D)  $( - \infty , \infty )$ 
E)  $( - \infty , 0 ]$

Determine $( g \circ f ) ( x )$ for the pair of functions $f ( x ) = 8 x + 3$ and $g ( x ) = x ^ { 2 } + 7$ .

Find the constant of variation for the stated condition: y varies directly as x , and y = 150 when x = 240.

Determine $( g \circ f ) ( x )$ for the pair of functions $f ( x ) = 5 x + 4$ and $g ( x ) = 3 x - 7$ .

Graph the function. $f ( x ) = \frac { 1 } { 6 } | x |$

Find $\frac { f ( a + h ) - f ( a ) } { h }$ for f ( x )= - x 2 - 7.

If you have the following function, f ( x )= -7| x | + 8, compute f (1), f (-3), f (2), f (-4)

Form the inverse function of the function and list the range of the inverse function. f = { (1, 8), (2, 9), (4, 11), (3, 7)}

Graph the function $y = \sqrt { x }$ .

Graph the function. Check your work with a graphing calculator. $f ( x ) = | x | + 7$

True or false? The function below is one-to-one function. f ( x )= - x ⁸

Find $\frac { f ( a + h ) - f ( a ) } { h }$ for f ( x )= x 2 - 8 x + 2.

Identify the graph of the function. f ( x )= -3 x ² - 6 x

If you have the following function, f ( x )= - x ² - 5 x + 4, compute f (3), f (-2), f (5), f (-4).

The linear depreciation method assumes that an item depreciates the same amount each year. Suppose a new piece of machinery costs $33,000 and it depreciates $850 each year for t years. Set up a linear function that yields the value of the machinery after t years.

Translate the statement of variation into an equation and use k as the constant of variation. A varies jointly as n and t .

Specify the domain of $( g \circ f ) ( x )$ for the pair of functions $f ( x ) = \frac { 7 } { 4 x }$ and $g ( x ) = \frac { 1 } { x + 3 }$ .

Translate the statement of variation into an equation and use k as the constant of variation. d varies directly as the cube of t .

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

Specify the domain of $( g \circ f ) ( x )$ for the pair of functions $f ( x ) = 3 x$ and $g ( x ) = 8 x - 7$ .

Basic Concepts and Properties

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Exam 9: Functions

Determine (g∘f)(x)( g \circ f ) ( x )(g∘f)(x) for the pair of functions f(x)=8x+3f ( x ) = 8 x + 3f(x)=8x+3 and g(x)=x2+7g ( x ) = x ^ { 2 } + 7g(x)=x2+7 .

Find the constant of variation for the stated condition: y varies directly as x , and y = 150 when x = 240.

Determine (g∘f)(x)( g \circ f ) ( x )(g∘f)(x) for the pair of functions f(x)=5x+4f ( x ) = 5 x + 4f(x)=5x+4 and g(x)=3x−7g ( x ) = 3 x - 7g(x)=3x−7 .

Graph the function. f(x)=16∣x∣f ( x ) = \frac { 1 } { 6 } | x |f(x)=61​∣x∣

Find f(a+h)−f(a)h\frac { f ( a + h ) - f ( a ) } { h }hf(a+h)−f(a)​ for f ( x )= - x 2 - 7.

If you have the following function, f ( x )= -7| x | + 8, compute f (1), f (-3), f (2), f (-4)

Form the inverse function of the function and list the range of the inverse function. f = { (1, 8), (2, 9), (4, 11), (3, 7)}

Graph the function y=xy = \sqrt { x }y=x​ .

Graph the function. Check your work with a graphing calculator. f(x)=∣x∣+7f ( x ) = | x | + 7f(x)=∣x∣+7

True or false? The function below is one-to-one function. f ( x )= - x 8

Find f(a+h)−f(a)h\frac { f ( a + h ) - f ( a ) } { h }hf(a+h)−f(a)​ for f ( x )= x 2 - 8 x + 2.

Identify the graph of the function. f ( x )= -3 x 2 - 6 x

If you have the following function, f ( x )= - x 2 - 5 x + 4, compute f (3), f (-2), f (5), f (-4).

The linear depreciation method assumes that an item depreciates the same amount each year. Suppose a new piece of machinery costs $33,000 and it depreciates $850 each year for t years. Set up a linear function that yields the value of the machinery after t years.

Translate the statement of variation into an equation and use k as the constant of variation. A varies jointly as n and t .

Specify the domain of (g∘f)(x)( g \circ f ) ( x )(g∘f)(x) for the pair of functions f(x)=74xf ( x ) = \frac { 7 } { 4 x }f(x)=4x7​ and g(x)=1x+3g ( x ) = \frac { 1 } { x + 3 }g(x)=x+31​ .

Translate the statement of variation into an equation and use k as the constant of variation. d varies directly as the cube of t .

Graph the function. f(x)=12x2f ( x ) = \frac { 1 } { 2 } x ^ { 2 }f(x)=21​x2

Specify the domain of (g∘f)(x)( g \circ f ) ( x )(g∘f)(x) for the pair of functions f(x)=3xf ( x ) = 3 xf(x)=3x and g(x)=8x−7g ( x ) = 8 x - 7g(x)=8x−7 .

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Conic Sections

Systems of Equations

Exponential and Logarithmic Functions

Filters

Determine $( g \circ f ) ( x )$ for the pair of functions $f ( x ) = 8 x + 3$ and $g ( x ) = x ^ { 2 } + 7$ .

Determine $( g \circ f ) ( x )$ for the pair of functions $f ( x ) = 5 x + 4$ and $g ( x ) = 3 x - 7$ .

Graph the function. $f ( x ) = \frac { 1 } { 6 } | x |$

Find $\frac { f ( a + h ) - f ( a ) } { h }$ for f ( x )= - x 2 - 7.

Graph the function $y = \sqrt { x }$ .

Graph the function. Check your work with a graphing calculator. $f ( x ) = | x | + 7$

True or false? The function below is one-to-one function. f ( x )= - x ⁸

Find $\frac { f ( a + h ) - f ( a ) } { h }$ for f ( x )= x 2 - 8 x + 2.

Identify the graph of the function. f ( x )= -3 x ² - 6 x

If you have the following function, f ( x )= - x ² - 5 x + 4, compute f (3), f (-2), f (5), f (-4).

Specify the domain of $( g \circ f ) ( x )$ for the pair of functions $f ( x ) = \frac { 7 } { 4 x }$ and $g ( x ) = \frac { 1 } { x + 3 }$ .

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

Specify the domain of $( g \circ f ) ( x )$ for the pair of functions $f ( x ) = 3 x$ and $g ( x ) = 8 x - 7$ .