Question 1

Graph the linear function. $$f ( x ) = - \frac { 3 } { 5 } x - 6$$

Accepted Answer

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

Question 2

Draw the graph using a translation of the graph of $f ( x ) = | x |$ . $f ( x ) = | x + 3 | + 4$

Accepted Answer

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

Question 3

At a constant temperature, the volume ( V )of a gas varies inversely as the pressure ( P ). Translate the statement of variation into an equation and use k as the constant of variation.

Accepted Answer

A)  $B = \frac { k } { H }$ 
B)  $k = \frac { H } { B }$ 
C)  $B = \frac { H } { k }$ 
D)  $H = k b$ 
E)  $H = \frac { k } { B }$ 
A)  $B = \frac { k } { H }$ 
B)  $k = \frac { H } { B }$ 
C)  $B = \frac { H } { k }$ 
D)  $H = k b$ 
E)  $H = \frac { k } { B }$

Question 4

Find the constant of variation for the stated condition: y varies inversely as x , and y = -144 when $x = \frac { 8 } { 7 }$ .

Accepted Answer

A)  $k = - \frac { 7 } { 8 }$ 
B)  $k = - 35 \frac { 8 } { 7 }$ 
C) k = 156 
D)  $k = - \frac { 8 } { 7 }$ 
E) k = -156 
A)  $k = - \frac { 7 } { 8 }$ 
B)  $k = - 35 \frac { 8 } { 7 }$ 
C) k = 156 
D)  $k = - \frac { 8 } { 7 }$ 
E) k = -156

Question 5

Sketch the graph of the associated function, $g ( x ) = | x |$ then draw the graph of the function f using translation and/or a reflection. $f ( x ) = | x - 4 | - 1$

Accepted Answer

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

Question 6

Determine whether the function is one-to-one. $$f ( x ) = x ^ { 8 } + 8$$

Accepted Answer

A) yes 
B) no 
A) yes 
B) no

Question 7

Graph the linear function. f ( x )= - 2

Accepted Answer

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

Question 8

Draw the graph using a translation of the graph of $f ( x ) = x ^ { 3 }$ . $f ( x ) = ( x + 4 ) ^ { 3 } - 1$

Accepted Answer

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

Question 9

Suppose that a car rental agency charges a fixed amount per day plus an amount per mile for renting a car. Heidi rented a car one day and paid $100.00 for 300 miles. On another day she rented a car from the same agency and paid $150.00 for 550 miles. Determine the linear function that the agency could use to determine its daily rental charges.

Accepted Answer

A) f ( x )= 0.4 x - 40 
B) f ( x )= 0.4 x + 40 
C) f ( x )= -0.2 x + 40 
D) f ( x )= 0.2 x - 40 
E) f ( x )= 0.2 x + 40 
A) f ( x )= 0.4 x - 40 
B) f ( x )= 0.4 x + 40 
C) f ( x )= -0.2 x + 40 
D) f ( x )= 0.2 x - 40 
E) f ( x )= 0.2 x + 40

Question 10

Find the inverse of the given function and express it in the form $y = f ^ { - 1 } ( x )$ . Verify the result by showing that $\left( f \circ f ^ { - 1 } \right) ( x ) = \left( f ^ { - 1 } \circ f \right) ( x ) = I ( x )$ . $f ( x ) = \frac { 2 x + 10 } { 5 }$

Accepted Answer

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

Question 11

Tell whether the equation determines y to be a function of x . $y ^ { 2 } = x + 7$

Accepted Answer

A) no 
B) yes 
A) no 
B) yes

Question 12

Form the inverse function of the function and list the domain of the inverse function. f = { (2, -6), (5, -8), (7, -2)}

Accepted Answer

A) { 2, -8, 7 } 
B) { 2, 5, -2 } 
C) { -6, 5, -2 } 
D) { 2, 5, 7 } 
E) { -6, -8, -2 } 
A) { 2, -8, 7 } 
B) { 2, 5, -2 } 
C) { -6, 5, -2 } 
D) { 2, 5, 7 } 
E) { -6, -8, -2 }

Question 13

Graph the function $y = x ^ { 3 }$ .

Accepted Answer

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

Question 14

Graph the function. Check your work with a graphing calculator. $f ( x ) = ( x + 3 ) ^ { 3 }$

Accepted Answer

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

Question 15

Specify the domain of $( g \circ f ) ( x )$ for the pair of functions $f ( x ) = 5 x + 6$ and $g ( x ) = x ^ { 2 } + 3$ .

Accepted Answer

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

Question 16

Determine whether the linear equation defines $y$ to be a function of $x$ . If so, find the domain and range. $y = \frac { 1 } { 3 } x - 1$

Accepted Answer

A) domain: $( - \infty , 0 )$ ; range: $( 0 , \infty )$ 
B) domain: $( 0 , \infty )$ ; range: $( - \infty , \infty )$ 
C) domain: $( - \infty , \infty )$ ; range: $( - \infty , \infty )$ 
D) domain: $( - \infty , \infty )$ ; range: $( 0 , \infty )$ 
E)  $y$ is not a function of $x$ 
A) domain: $( - \infty , 0 )$ ; range: $( 0 , \infty )$ 
B) domain: $( 0 , \infty )$ ; range: $( - \infty , \infty )$ 
C) domain: $( - \infty , \infty )$ ; range: $( - \infty , \infty )$ 
D) domain: $( - \infty , \infty )$ ; range: $( 0 , \infty )$ 
E)  $y$ is not a function of $x$

Question 17

Graph the function. Check your work with a graphing calculator. f ( x )= x  2 + 5

Accepted Answer

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

Question 18

Graph the linear function. f ( x )= 3 x + 9

Accepted Answer

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

Question 19

Find the constant of variation for the stated condition: A varies jointly as b and h , and A = 48 when b = 64 and h = 2.

Accepted Answer

A)  $k = 3$ 
B)  $k = 5$ 
C)  $k = - \frac { 4 } { 3 }$ 
D)  $k = \frac { 3 } { 4 }$ 
E)  $k = \frac { 4 } { 3 }$ 
A)  $k = 3$ 
B)  $k = 5$ 
C)  $k = - \frac { 4 } { 3 }$ 
D)  $k = \frac { 3 } { 4 }$ 
E)  $k = \frac { 4 } { 3 }$

Question 20

Graph the function $y = - | x |$ .

Accepted Answer

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

Graph the linear function. $f ( x ) = - \frac { 3 } { 5 } x - 6$

Draw the graph using a translation of the graph of $f ( x ) = | x |$ . $f ( x ) = | x + 3 | + 4$

At a constant temperature, the volume ( V )of a gas varies inversely as the pressure ( P ). Translate the statement of variation into an equation and use k as the constant of variation.

Find the constant of variation for the stated condition: y varies inversely as x , and y = -144 when $x = \frac { 8 } { 7 }$ .

Sketch the graph of the associated function, $g ( x ) = | x |$ then draw the graph of the function f using translation and/or a reflection. $f ( x ) = | x - 4 | - 1$

Determine whether the function is one-to-one. $f ( x ) = x ^ { 8 } + 8$

Graph the linear function. f ( x )= - 2

Draw the graph using a translation of the graph of $f ( x ) = x ^ { 3 }$ . $f ( x ) = ( x + 4 ) ^ { 3 } - 1$

Find the inverse of the given function and express it in the form $y = f ^ { - 1 } ( x )$ . Verify the result by showing that $\left( f \circ f ^ { - 1 } \right) ( x ) = \left( f ^ { - 1 } \circ f \right) ( x ) = I ( x )$ . $f ( x ) = \frac { 2 x + 10 } { 5 }$

Tell whether the equation determines y to be a function of x . $y ^ { 2 } = x + 7$

Form the inverse function of the function and list the domain of the inverse function. f = { (2, -6), (5, -8), (7, -2)}

Graph the function $y = x ^ { 3 }$ .

Graph the function. Check your work with a graphing calculator. $f ( x ) = ( x + 3 ) ^ { 3 }$

Specify the domain of $( g \circ f ) ( x )$ for the pair of functions $f ( x ) = 5 x + 6$ and $g ( x ) = x ^ { 2 } + 3$ .

Determine whether the linear equation defines $y$ to be a function of $x$ . If so, find the domain and range. $y = \frac { 1 } { 3 } x - 1$ $Determine whether the linear equation defines y to be a function of x . If so, find the domain and range. y = \frac { 1 } { 3 } x - 1$

Graph the function. Check your work with a graphing calculator. f ( x )= x ²+ 5

Graph the linear function. f ( x )= 3 x + 9

Find the constant of variation for the stated condition: A varies jointly as b and h , and A = 48 when b = 64 and h = 2.

Graph the function $y = - | x |$ .

Basic Concepts and Properties

Equations, Inequalities, and Problem Solving

Polynomials

Rational Expressions

Exponents and Radicals

Quadratic Equations and Inequalities

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Exam 9: Functions

Graph the linear function. f(x)=−35x−6f ( x ) = - \frac { 3 } { 5 } x - 6f(x)=−53​x−6

Draw the graph using a translation of the graph of f(x)=∣x∣f ( x ) = | x |f(x)=∣x∣ . f(x)=∣x+3∣+4f ( x ) = | x + 3 | + 4f(x)=∣x+3∣+4

At a constant temperature, the volume ( V )of a gas varies inversely as the pressure ( P ). Translate the statement of variation into an equation and use k as the constant of variation.

Find the constant of variation for the stated condition: y varies inversely as x , and y = -144 when x=87x = \frac { 8 } { 7 }x=78​ .

Sketch the graph of the associated function, g(x)=∣x∣g ( x ) = | x |g(x)=∣x∣ then draw the graph of the function f using translation and/or a reflection. f(x)=∣x−4∣−1f ( x ) = | x - 4 | - 1f(x)=∣x−4∣−1

Determine whether the function is one-to-one. f(x)=x8+8f ( x ) = x ^ { 8 } + 8f(x)=x8+8

Graph the linear function. f ( x )= - 2

Draw the graph using a translation of the graph of f(x)=x3f ( x ) = x ^ { 3 }f(x)=x3 . f(x)=(x+4)3−1f ( x ) = ( x + 4 ) ^ { 3 } - 1f(x)=(x+4)3−1

Tell whether the equation determines y to be a function of x . y2=x+7y ^ { 2 } = x + 7y2=x+7

Form the inverse function of the function and list the domain of the inverse function. f = { (2, -6), (5, -8), (7, -2)}

Graph the function y=x3y = x ^ { 3 }y=x3 .

Graph the function. Check your work with a graphing calculator. f(x)=(x+3)3f ( x ) = ( x + 3 ) ^ { 3 }f(x)=(x+3)3

Specify the domain of (g∘f)(x)( g \circ f ) ( x )(g∘f)(x) for the pair of functions f(x)=5x+6f ( x ) = 5 x + 6f(x)=5x+6 and g(x)=x2+3g ( x ) = x ^ { 2 } + 3g(x)=x2+3 .

Determine whether the linear equation defines yyy to be a function of xxx . If so, find the domain and range. y=13x−1y = \frac { 1 } { 3 } x - 1y=31​x−1

Graph the function. Check your work with a graphing calculator. f ( x )= x 2 + 5

Graph the linear function. f ( x )= 3 x + 9

Find the constant of variation for the stated condition: A varies jointly as b and h , and A = 48 when b = 64 and h = 2.

Graph the function y=−∣x∣y = - | x |y=−∣x∣ .

Basic Concepts and Properties

Equations, Inequalities, and Problem Solving

Polynomials

Rational Expressions

Exponents and Radicals

Quadratic Equations and Inequalities

Equations and Inequalities in Two Variables

Conic Sections

Systems of Equations

Exponential and Logarithmic Functions

Filters

Graph the linear function. $f ( x ) = - \frac { 3 } { 5 } x - 6$

Draw the graph using a translation of the graph of $f ( x ) = | x |$ . $f ( x ) = | x + 3 | + 4$

Find the constant of variation for the stated condition: y varies inversely as x , and y = -144 when $x = \frac { 8 } { 7 }$ .

Sketch the graph of the associated function, $g ( x ) = | x |$ then draw the graph of the function f using translation and/or a reflection. $f ( x ) = | x - 4 | - 1$

Determine whether the function is one-to-one. $f ( x ) = x ^ { 8 } + 8$

Draw the graph using a translation of the graph of $f ( x ) = x ^ { 3 }$ . $f ( x ) = ( x + 4 ) ^ { 3 } - 1$

Tell whether the equation determines y to be a function of x . $y ^ { 2 } = x + 7$

Graph the function $y = x ^ { 3 }$ .

Graph the function. Check your work with a graphing calculator. $f ( x ) = ( x + 3 ) ^ { 3 }$

Specify the domain of $( g \circ f ) ( x )$ for the pair of functions $f ( x ) = 5 x + 6$ and $g ( x ) = x ^ { 2 } + 3$ .

Determine whether the linear equation defines $y$ to be a function of $x$ . If so, find the domain and range. $y = \frac { 1 } { 3 } x - 1$ $Determine whether the linear equation defines y to be a function of x . If so, find the domain and range. y = \frac { 1 } { 3 } x - 1$

Graph the function. Check your work with a graphing calculator. f ( x )= x ²+ 5

Graph the function $y = - | x |$ .