Question 1

The graph of the function $g ( x )$ is a translation of the graph of $f ( x ) = x ^ { 3 }$. Graph the function.

Accepted Answer

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

Question 2

Let $f ( x ) = \sqrt { x + 1 } , g ( x ) = x ^ { 2 } - 1$. Find the domain of the composite function. $( f \circ g ) ( x )$

Accepted Answer

A)  $\quad ( - 1 , \infty )$ 
B)  $\quad ( - \infty , - 1 ]$ 
C)  $\quad ( - \infty , - 1 )$ 
D)  $[ - 1 , \infty )$ 
E)  $\quad ( - \infty , \infty )$ 
A)  $\quad ( - 1 , \infty )$ 
B)  $\quad ( - \infty , - 1 ]$ 
C)  $\quad ( - \infty , - 1 )$ 
D)  $[ - 1 , \infty )$ 
E)  $\quad ( - \infty , \infty )$ E

Question 3

Graph the rational function. $$f ( x ) = \frac { 2 x ^ { 3 } + 4 x } { 5 x }$$
Note that the numerator and denominator of the fraction share a common factor.

Accepted Answer

A) 
  
B) 
  
C)

$\mathrm { d } .$
  
A) 
  
B) 
  
C)

$\mathrm { d } .$
  B

Question 4

Let $f ( x ) = 3 x , g ( x ) = x + 1$. Find the composite function.
$$( g \circ g ) ( x )$$

Accepted Answer

A)  $\quad ( g \circ g ) ( x ) = 3 x + 1$ 
B)  none of the above 
C)  $\quad ( g \circ g ) ( x ) = 3 x + 3$ 
D)  $\quad ( g \circ g ) ( x ) = 9 x$ 
E)  $\quad ( g \circ g ) ( x ) = x + 2$ 
A)  $\quad ( g \circ g ) ( x ) = 3 x + 1$ 
B)  none of the above 
C)  $\quad ( g \circ g ) ( x ) = 3 x + 3$ 
D)  $\quad ( g \circ g ) ( x ) = 9 x$ 
E)  $\quad ( g \circ g ) ( x ) = x + 2$

Question 5

Let $f ( x ) = \sqrt { x } , g ( x ) = x + 2$. Find the composite function which expresses the given correspondence correctly.
$\sqrt [ 4 ] { x }$

Accepted Answer

A)  $\quad ( f \circ f ) ( x )$ 
B)  $\quad ( f \circ g ) ( x )$ 
C)  $( g \circ f ) ( x )$ 
D)  none of the above 
E)  $( g \circ g ) ( x )$ 
A)  $\quad ( f \circ f ) ( x )$ 
B)  $\quad ( f \circ g ) ( x )$ 
C)  $( g \circ f ) ( x )$ 
D)  none of the above 
E)  $( g \circ g ) ( x )$

Question 6

Let $f ( x ) = \sqrt { x + 1 } , g ( x ) = x ^ { 2 } - 1$. Find the domain of the composite function.
$$( f \circ g ) ( x )$$

Accepted Answer

A)  $\quad ( - \infty , - 1 )$ 
B)  $\quad ( - \infty , - 1 ]$ 
C)  $\quad ( - \infty , \infty )$ 
D)  $\quad ( - 1 , \infty )$ 
E)  $[ - 1 , \infty )$ 
A)  $\quad ( - \infty , - 1 )$ 
B)  $\quad ( - \infty , - 1 ]$ 
C)  $\quad ( - \infty , \infty )$ 
D)  $\quad ( - 1 , \infty )$ 
E)  $[ - 1 , \infty )$

Question 7

Graph the quadratic function. $$f ( x ) = - 4 x ^ { 2 } + 2$$

Accepted Answer

A) 
  
B) 
  
C) 
 
$\mathrm { d }$.
  
A) 
  
B) 
  
C) 
 
$\mathrm { d }$.

Question 8

The graph of the function $g ( x )$ is a translation of the graph of $f ( x ) = x ^ { 3 }$. Graph the function. $g ( x ) = ( x - 3 ) ^ { 3 } - 2$

Accepted Answer

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

Question 9

A 270-room hotel is two-thirds filled when the nightly room rate is $100.Experience has shown that each $10 increase in cost results in 20 fewer occupied rooms.Find the nightly rate that will maximize
Income.

Accepted Answer

A)  $\$ 45.00$ 
B)  $\$ 285.00$ 
C)  $\$ 95.00$ 
D)  $\$ 190.00$ 
E)  $\$ 117.50$ 
A)  $\$ 45.00$ 
B)  $\$ 285.00$ 
C)  $\$ 95.00$ 
D)  $\$ 190.00$ 
E)  $\$ 117.50$

Question 10

The graph of the function $f ( x )$ is a translation of the graph of $y = ( x - 1 ) ^ { 2 }$. Graph the function. $f ( x ) = ( - x - 1 ) ^ { 2 }$

Accepted Answer

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

Question 11

Let $f ( x ) = \sqrt { x } , g ( x ) = x + 2$. Find the composite function which expresses the given correspondence correctly.
$\sqrt [ 4 ] { x }$

Accepted Answer

A)  $\quad ( g \circ g ) ( x )$ 
B)  $( f \circ f ) ( x )$ 
C)  $\quad ( g \circ f ) ( x )$ 
D)  $\quad ( f \circ g ) ( x )$ 
E)  none of the above 
A)  $\quad ( g \circ g ) ( x )$ 
B)  $( f \circ f ) ( x )$ 
C)  $\quad ( g \circ f ) ( x )$ 
D)  $\quad ( f \circ g ) ( x )$ 
E)  none of the above

Question 12

Evaluate the difference quotient for the function. $$f ( x ) = 3 x ^ { 2 } - 20$$

Accepted Answer

A)  3 
B)  $\quad 1$ 
C)  $\quad 6$ 
D)  $\quad 3 x + h$ 
E)  $\quad 6 x + 3 h$ 
A)  3 
B)  $\quad 1$ 
C)  $\quad 6$ 
D)  $\quad 3 x + h$ 
E)  $\quad 6 x + 3 h$

Question 13

The amount $A$ of money on deposit for $t$ years in an account earning simple interest is a linear function of $t$. Express that function as an equation if $A = \$ 85$ when $t = 8$ and $A = \$ 40$ when $t = 3$.

Accepted Answer

A)  $A = 40 t - 13$ 
B)  $A = 9 t + 13$ 
C)  $A = - 9 t + 13$ 
D)  $A = 9 t - 13$ 
E)  $A = 40 t + 13$ 
A)  $A = 40 t - 13$ 
B)  $A = 9 t + 13$ 
C)  $A = - 9 t + 13$ 
D)  $A = 9 t - 13$ 
E)  $A = 40 t + 13$

Question 14

Graph the quadratic function. $$f ( x ) = - 3 x ^ { 2 } + 2$$

Accepted Answer

A) 
  
B) 
  
C) 
 
$\mathrm { d }$.
  
A) 
  
B) 
  
C) 
 
$\mathrm { d }$.

Question 15

Let $f ( x ) = 3 x , g ( x ) = x + 1$. Find the composite function.
$$( g \circ g ) ( x )$$

Accepted Answer

A)  $\quad ( g \circ g ) ( x ) = 9 x$ 
B)  $\quad ( g \circ g ) ( x ) = 3 x + 3$ 
C)  $\quad ( g \circ g ) ( x ) = 3 x + 1$ 
D)  $\quad ( g \circ g ) ( x ) = x + 2$ 
E)  none of the above 
A)  $\quad ( g \circ g ) ( x ) = 9 x$ 
B)  $\quad ( g \circ g ) ( x ) = 3 x + 3$ 
C)  $\quad ( g \circ g ) ( x ) = 3 x + 1$ 
D)  $\quad ( g \circ g ) ( x ) = x + 2$ 
E)  none of the above

Question 16

Evaluate the difference quotient for the function. $$f ( x ) = 4 x ^ { 2 } - 5$$

Accepted Answer

A)  $\quad 8 x + 4 h$ 
B)  1 
C)  $\quad 8$ 
D)  $4 x + h$ 
E)  4 
A)  $\quad 8 x + 4 h$ 
B)  1 
C)  $\quad 8$ 
D)  $4 x + h$ 
E)  4

Question 17

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

Accepted Answer

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

Question 18

Graph the quadratic function. $$f ( x ) = - x ^ { 2 } - 3 x + 2$$

Accepted Answer

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

Question 19

The graph of the function $g ( x )$ is a translation of the graph of $f ( x ) = x ^ { 3 }$. Graph the function. $g ( x ) = ( x - 3 ) ^ { 3 }$

Accepted Answer

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

Question 20

Let $f ( x ) = \sqrt { x + 1 } , g ( x ) = x ^ { 2 } - 1$. Find the domain of the composite function. $( g \circ f ) ( x )$

Accepted Answer

A)  $[ - 1 , \infty )$ 
B)  $\quad ( - \infty , - 1 ]$ 
C)  $\quad ( - \infty , - 1 )$ 
D)  $( - \infty , \infty )$ 
E)  $( - 1 , \infty )$ 
A)  $[ - 1 , \infty )$ 
B)  $\quad ( - \infty , - 1 ]$ 
C)  $\quad ( - \infty , - 1 )$ 
D)  $( - \infty , \infty )$ 
E)  $( - 1 , \infty )$

The graph of the function $g ( x )$ is a translation of the graph of $f ( x ) = x ^ { 3 }$ . Graph the function.

Let $f ( x ) = \sqrt { x + 1 } , g ( x ) = x ^ { 2 } - 1$ . Find the domain of the composite function. $( f \circ g ) ( x )$

Graph the rational function. $f ( x ) = \frac { 2 x ^ { 3 } + 4 x } { 5 x }$ Note that the numerator and denominator of the fraction share a common factor.

Let $f ( x ) = 3 x , g ( x ) = x + 1$ . Find the composite function. $( g \circ g ) ( x )$

Let $f ( x ) = \sqrt { x } , g ( x ) = x + 2$ . Find the composite function which expresses the given correspondence correctly. $\sqrt [ 4 ] { x }$

Let $f ( x ) = \sqrt { x + 1 } , g ( x ) = x ^ { 2 } - 1$ . Find the domain of the composite function. $( f \circ g ) ( x )$

Graph the quadratic function. $f ( x ) = - 4 x ^ { 2 } + 2$

The graph of the function $g ( x )$ is a translation of the graph of $f ( x ) = x ^ { 3 }$ . Graph the function. $g ( x ) = ( x - 3 ) ^ { 3 } - 2$

A 270-room hotel is two-thirds filled when the nightly room rate is $100.Experience has shown that each $10 increase in cost results in 20 fewer occupied rooms.Find the nightly rate that will maximize Income.

The graph of the function $f ( x )$ is a translation of the graph of $y = ( x - 1 ) ^ { 2 }$ . Graph the function. $f ( x ) = ( - x - 1 ) ^ { 2 }$

Let $f ( x ) = \sqrt { x } , g ( x ) = x + 2$ . Find the composite function which expresses the given correspondence correctly. $\sqrt [ 4 ] { x }$

Evaluate the difference quotient for the function. $f ( x ) = 3 x ^ { 2 } - 20$

The amount $A$ of money on deposit for $t$ years in an account earning simple interest is a linear function of $t$ . Express that function as an equation if $A = \$ 85$ when $t = 8$ and $A = \$ 40$ when $t = 3$ .

Graph the quadratic function. $f ( x ) = - 3 x ^ { 2 } + 2$

Let $f ( x ) = 3 x , g ( x ) = x + 1$ . Find the composite function. $( g \circ g ) ( x )$

Evaluate the difference quotient for the function. $f ( x ) = 4 x ^ { 2 } - 5$

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

Graph the quadratic function. $f ( x ) = - x ^ { 2 } - 3 x + 2$

The graph of the function $g ( x )$ is a translation of the graph of $f ( x ) = x ^ { 3 }$ . Graph the function. $g ( x ) = ( x - 3 ) ^ { 3 }$

Let $f ( x ) = \sqrt { x + 1 } , g ( x ) = x ^ { 2 } - 1$ . Find the domain of the composite function. $( g \circ f ) ( x )$

A Review of Basic Algebra

Equations and Inequalities

The Rectangular Coordinate System and Graphs of Equations

Exponential and Logarithmic Functions

Solving Polynomial Equations

Linear Systems

Conic Sections and Quadratic Systems

Natural Number Functions and Probability

Filters

Exam 4: Functions Functions and Function Notation

The graph of the function g(x)g ( x )g(x) is a translation of the graph of f(x)=x3f ( x ) = x ^ { 3 }f(x)=x3 . Graph the function.

Let f(x)=x+1,g(x)=x2−1f ( x ) = \sqrt { x + 1 } , g ( x ) = x ^ { 2 } - 1f(x)=x+1​,g(x)=x2−1 . Find the domain of the composite function. (f∘g)(x)( f \circ g ) ( x )(f∘g)(x)

Graph the rational function. f(x)=2x3+4x5xf ( x ) = \frac { 2 x ^ { 3 } + 4 x } { 5 x }f(x)=5x2x3+4x​ Note that the numerator and denominator of the fraction share a common factor.

Let f(x)=3x,g(x)=x+1f ( x ) = 3 x , g ( x ) = x + 1f(x)=3x,g(x)=x+1 . Find the composite function. (g∘g)(x)( g \circ g ) ( x )(g∘g)(x)

Let f(x)=x,g(x)=x+2f ( x ) = \sqrt { x } , g ( x ) = x + 2f(x)=x​,g(x)=x+2 . Find the composite function which expresses the given correspondence correctly. x4\sqrt [ 4 ] { x }4x​

Let f(x)=x+1,g(x)=x2−1f ( x ) = \sqrt { x + 1 } , g ( x ) = x ^ { 2 } - 1f(x)=x+1​,g(x)=x2−1 . Find the domain of the composite function. (f∘g)(x)( f \circ g ) ( x )(f∘g)(x)

Graph the quadratic function. f(x)=−4x2+2f ( x ) = - 4 x ^ { 2 } + 2f(x)=−4x2+2

The graph of the function g(x)g ( x )g(x) is a translation of the graph of f(x)=x3f ( x ) = x ^ { 3 }f(x)=x3 . Graph the function. g(x)=(x−3)3−2g ( x ) = ( x - 3 ) ^ { 3 } - 2g(x)=(x−3)3−2

A 270-room hotel is two-thirds filled when the nightly room rate is $100.Experience has shown that each $10 increase in cost results in 20 fewer occupied rooms.Find the nightly rate that will maximize Income.

The graph of the function f(x)f ( x )f(x) is a translation of the graph of y=(x−1)2y = ( x - 1 ) ^ { 2 }y=(x−1)2 . Graph the function. f(x)=(−x−1)2f ( x ) = ( - x - 1 ) ^ { 2 }f(x)=(−x−1)2

Let f(x)=x,g(x)=x+2f ( x ) = \sqrt { x } , g ( x ) = x + 2f(x)=x​,g(x)=x+2 . Find the composite function which expresses the given correspondence correctly. x4\sqrt [ 4 ] { x }4x​

Evaluate the difference quotient for the function. f(x)=3x2−20f ( x ) = 3 x ^ { 2 } - 20f(x)=3x2−20

The amount AAA of money on deposit for ttt years in an account earning simple interest is a linear function of ttt . Express that function as an equation if A=$85A = \$ 85A=$85 when t=8t = 8t=8 and A=$40A = \$ 40A=$40 when t=3t = 3t=3 .

Graph the quadratic function. f(x)=−3x2+2f ( x ) = - 3 x ^ { 2 } + 2f(x)=−3x2+2

Let f(x)=3x,g(x)=x+1f ( x ) = 3 x , g ( x ) = x + 1f(x)=3x,g(x)=x+1 . Find the composite function. (g∘g)(x)( g \circ g ) ( x )(g∘g)(x)

Evaluate the difference quotient for the function. f(x)=4x2−5f ( x ) = 4 x ^ { 2 } - 5f(x)=4x2−5

The function f(x)=x2−5f ( x ) = \sqrt { x ^ { 2 } - 5 }f(x)=x2−5​ is one-to-one on the domain x≤−5x \leq - \sqrt { 5 }x≤−5​ . Find f−1(x)f ^ { - 1 } ( x )f−1(x) .

Graph the quadratic function. f(x)=−x2−3x+2f ( x ) = - x ^ { 2 } - 3 x + 2f(x)=−x2−3x+2

The graph of the function g(x)g ( x )g(x) is a translation of the graph of f(x)=x3f ( x ) = x ^ { 3 }f(x)=x3 . Graph the function. g(x)=(x−3)3g ( x ) = ( x - 3 ) ^ { 3 }g(x)=(x−3)3

Let f(x)=x+1,g(x)=x2−1f ( x ) = \sqrt { x + 1 } , g ( x ) = x ^ { 2 } - 1f(x)=x+1​,g(x)=x2−1 . Find the domain of the composite function. (g∘f)(x)( g \circ f ) ( x )(g∘f)(x)

A Review of Basic Algebra

Equations and Inequalities

The Rectangular Coordinate System and Graphs of Equations

Exponential and Logarithmic Functions

Solving Polynomial Equations

Linear Systems

Conic Sections and Quadratic Systems

Natural Number Functions and Probability

Filters

The graph of the function $g ( x )$ is a translation of the graph of $f ( x ) = x ^ { 3 }$ . Graph the function.

Let $f ( x ) = \sqrt { x + 1 } , g ( x ) = x ^ { 2 } - 1$ . Find the domain of the composite function. $( f \circ g ) ( x )$

Graph the rational function. $f ( x ) = \frac { 2 x ^ { 3 } + 4 x } { 5 x }$ Note that the numerator and denominator of the fraction share a common factor.

Let $f ( x ) = 3 x , g ( x ) = x + 1$ . Find the composite function. $( g \circ g ) ( x )$

Let $f ( x ) = \sqrt { x } , g ( x ) = x + 2$ . Find the composite function which expresses the given correspondence correctly. $\sqrt [ 4 ] { x }$

Let $f ( x ) = \sqrt { x + 1 } , g ( x ) = x ^ { 2 } - 1$ . Find the domain of the composite function. $( f \circ g ) ( x )$

Graph the quadratic function. $f ( x ) = - 4 x ^ { 2 } + 2$

The graph of the function $g ( x )$ is a translation of the graph of $f ( x ) = x ^ { 3 }$ . Graph the function. $g ( x ) = ( x - 3 ) ^ { 3 } - 2$

The graph of the function $f ( x )$ is a translation of the graph of $y = ( x - 1 ) ^ { 2 }$ . Graph the function. $f ( x ) = ( - x - 1 ) ^ { 2 }$

Let $f ( x ) = \sqrt { x } , g ( x ) = x + 2$ . Find the composite function which expresses the given correspondence correctly. $\sqrt [ 4 ] { x }$

Evaluate the difference quotient for the function. $f ( x ) = 3 x ^ { 2 } - 20$

The amount $A$ of money on deposit for $t$ years in an account earning simple interest is a linear function of $t$ . Express that function as an equation if $A = \$ 85$ when $t = 8$ and $A = \$ 40$ when $t = 3$ .

Graph the quadratic function. $f ( x ) = - 3 x ^ { 2 } + 2$

Let $f ( x ) = 3 x , g ( x ) = x + 1$ . Find the composite function. $( g \circ g ) ( x )$

Evaluate the difference quotient for the function. $f ( x ) = 4 x ^ { 2 } - 5$

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

Graph the quadratic function. $f ( x ) = - x ^ { 2 } - 3 x + 2$

The graph of the function $g ( x )$ is a translation of the graph of $f ( x ) = x ^ { 3 }$ . Graph the function. $g ( x ) = ( x - 3 ) ^ { 3 }$

Let $f ( x ) = \sqrt { x + 1 } , g ( x ) = x ^ { 2 } - 1$ . Find the domain of the composite function. $( g \circ f ) ( x )$