Question 1

Graph the function. $$y = [ [ 3 x ] ]$$

Accepted Answer

A) 
  
B) 
  
C)

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

$\mathrm { d }$.

Question 2

Find the range of the function $f ( x ) = \frac { 4 x } { x - 2 }$ by finding the domain of $f ^ { - 1 } ( x )$.

Accepted Answer

A)  $\quad ( - \infty , 2 ) \cup ( 2 , \infty )$ 
B)  $\quad ( - \infty , 4 ) \cup ( 4 , \infty )$ 
C)  $\quad ( - \infty , \infty )$ 
D)  $\quad ( - \infty , 0 ) \cup ( 0 , \infty )$ 
E)  $\quad ( 0 , \infty )$ 
A)  $\quad ( - \infty , 2 ) \cup ( 2 , \infty )$ 
B)  $\quad ( - \infty , 4 ) \cup ( 4 , \infty )$ 
C)  $\quad ( - \infty , \infty )$ 
D)  $\quad ( - \infty , 0 ) \cup ( 0 , \infty )$ 
E)  $\quad ( 0 , \infty )$

Question 3

A taxicab company charges $\$ 6$ for a trip up to 1 mile, and $\$ 5$ for every extra mile (or portion of a mile). Graph the ordered pairs $( m , c )$, where $m$ represents the miles traveled and $c$ represents the cost.

Accepted Answer

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

Question 4

The graph of the function $g ( x )$ is a translation of the graph of $f ( x ) = x ^ { 3 }$. Graph the function. $g ( x ) = ( x - 2 ) ^ { 3 } - 5$

Accepted Answer

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

Question 5

At a time t seconds after an object is tossed vertically upward, it reaches a height s in feet given by the equation: $s = 320 t - 16 t ^ { 2 }$
In how many seconds does the object reach its maximum height?

Accepted Answer

A)  800 sec 
B)  1,600 sec 
C)  10 sec 
D)  5 sec 
A)  800 sec 
B)  1,600 sec 
C)  10 sec 
D)  5 sec

Question 6

The graph of the function $g ( x )$ is a translation of the graph of $f ( x ) = x ^ { 2 }$. Graph the function. $g ( x ) = ( x + 4 ) ^ { 2 } + 3$

Accepted Answer

A) 
  
B) 
  
C)

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

$\mathrm { d }$.

Question 7

Evaluate the difference quotient for the function. $$f ( x ) = 4 x ^ { 2 } - 14$$

Accepted Answer

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

Question 8

The graph of the function $g ( x )$ is a translation of the graph of $f ( x ) = x ^ { 2 }$. Graph the function. $g ( x ) = ( x + 1 ) ^ { 2 } + 3$

Accepted Answer

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

Question 9

Graph the function.
$$f ( x ) = \frac { x ^ { 2 } - 2 x - 3 } { x ^ { 2 } - 3 x + 5 }$$

Accepted Answer

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

Question 10

At a time $t$ seconds after an object is tossed vertically upward, it reaches a height $s$ in feet given by the equation:
$$s = 128 t - 16 t ^ { 2 }$$
In how many seconds does the object reach its maximum height?

Accepted Answer

A)  $\quad 8 \mathrm { sec }$ 
B)  $\quad 128 \mathrm { sec }$ 
C)  $\quad 4 \mathrm { sec }$ 
D)  $256 \mathrm { sec }$ 
E)  $\quad 2 \mathrm { sec }$ 
A)  $\quad 8 \mathrm { sec }$ 
B)  $\quad 128 \mathrm { sec }$ 
C)  $\quad 4 \mathrm { sec }$ 
D)  $256 \mathrm { sec }$ 
E)  $\quad 2 \mathrm { sec }$

Question 11

Find the inverse of the one-to-one function. $$y = 3 x + 9$$

Accepted Answer

A)  $\quad y = \frac { x + 9 } { 3 }$ 
B)  $\quad y = \frac { x - 3 } { 9 }$ 
C)  $\quad y = \frac { 3 } { x - 9 }$ 
D)  $\quad y = \frac { x - 9 } { 3 }$ 
E)  none of the above 
A)  $\quad y = \frac { x + 9 } { 3 }$ 
B)  $\quad y = \frac { x - 3 } { 9 }$ 
C)  $\quad y = \frac { 3 } { x - 9 }$ 
D)  $\quad y = \frac { x - 9 } { 3 }$ 
E)  none of the above

Question 12

Graph the function. $$y = [ [ 3 x ] ]$$

Accepted Answer

A) 
  
B) 
  
C)

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

$\mathrm { d }$.

Question 13

A 330-room hotel is two-thirds filled when the nightly room rate is $70.Experience has shown that each $5 increase in cost results in 10 fewer occupied rooms.Find the nightly rate that will maximize
Income.

Accepted Answer

A)  $\$ 55.00$ 
B)  $\$ 180.00$ 
C)  $\$ 90.00$ 
D)  $\$ 270.00$ 
E)  $ \$ 117.50$ 
A)  $\$ 55.00$ 
B)  $\$ 180.00$ 
C)  $\$ 90.00$ 
D)  $\$ 270.00$ 
E)  $ \$ 117.50$

Question 14

Find the range of the function $f ( x ) = \frac { 4 x } { x - 5 }$ by finding the domain of $f ^ { - 1 } ( x )$.

Accepted Answer

A)  $\quad ( - \infty , \infty )$ 
B)  $\quad ( - \infty , 0 ) \cup ( 0 , \infty )$ 
C)  $\quad ( - \infty , 4 ) \cup ( 4 , \infty )$ 
D)  $\quad ( 0 , \infty )$ 
E)  $\quad ( - \infty , 5 ) \cup ( 5 , \infty )$ 
A)  $\quad ( - \infty , \infty )$ 
B)  $\quad ( - \infty , 0 ) \cup ( 0 , \infty )$ 
C)  $\quad ( - \infty , 4 ) \cup ( 4 , \infty )$ 
D)  $\quad ( 0 , \infty )$ 
E)  $\quad ( - \infty , 5 ) \cup ( 5 , \infty )$

Question 15

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

Accepted Answer

A)  $y = \frac { 5 } { x }$ 
B)  $y = 25 x$ 
C)  $y = 5 x ^ { 2 }$ 
D)  $\quad y = \frac { x } { 5 }$ 
E)  $\quad y = 5 x$ 
A)  $y = \frac { 5 } { x }$ 
B)  $y = 25 x$ 
C)  $y = 5 x ^ { 2 }$ 
D)  $\quad y = \frac { x } { 5 }$ 
E)  $\quad y = 5 x$

Question 16

Determine whether the function is one-to-one. $$y = \frac { 2 } { 9 } x$$

Accepted Answer

A)  No, it isn't one-to-one. 
B)  Yes, it is one-to-one. 
A)  No, it isn't one-to-one. 
B)  Yes, it is one-to-one.

Question 17

Find the vertex of the parabola. $$y = 2 x ^ { 2 } - 5$$

Accepted Answer

A)  $\quad ( 0,2 )$ 
B)  $\quad ( 2 , - 5 )$ 
C)  $\quad ( - 5,2 )$ 
D)  $\quad ( - 5,0 )$ 
E)  $\quad ( 0 , - 5 )$ 
A)  $\quad ( 0,2 )$ 
B)  $\quad ( 2 , - 5 )$ 
C)  $\quad ( - 5,2 )$ 
D)  $\quad ( - 5,0 )$ 
E)  $\quad ( 0 , - 5 )$

Question 18

A pizzeria charges $\$ 12.50$ plus $\$ 0.60$ per topping for a large pizza. Find the cost of a pizza that has 3 toppings.

Accepted Answer

A)  $\quad \$ 10.70$ 
B)  $\$ 14.30$ 
C)  $\$ 15.30$ 
D)  $\$ 15.65$ 
E)  $\$ 10.45$ 
A)  $\quad \$ 10.70$ 
B)  $\$ 14.30$ 
C)  $\$ 15.30$ 
D)  $\$ 15.65$ 
E)  $\$ 10.45$

Question 19

A taxicab company charges $\$ 3$ for a trip up to 1 mile, and $\$ 2$ for every extra mile (or portion of a mile). Graph the ordered pairs $( m , c )$, where $m$ represents the miles traveled and $c$ represents the cost.

Accepted Answer

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

Question 20

Let $f ( x ) = 2 x - 1 , g ( x ) = 3 x - 2$. Find the domain of the function.
$$( f \cdot g ) ( x )$$

Accepted Answer

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

Graph the function. $y = [ [ 3 x ] ]$

Find the range of the function $f ( x ) = \frac { 4 x } { x - 2 }$ by finding the domain of $f ^ { - 1 } ( x )$ .

A taxicab company charges $\$ 6$ for a trip up to 1 mile, and $\$ 5$ for every extra mile (or portion of a mile). Graph the ordered pairs $( m , c )$ , where $m$ represents the miles traveled and $c$ represents the cost.

The graph of the function $g ( x )$ is a translation of the graph of $f ( x ) = x ^ { 3 }$ . Graph the function. $g ( x ) = ( x - 2 ) ^ { 3 } - 5$

At a time t seconds after an object is tossed vertically upward, it reaches a height s in feet given by the equation: $s = 320 t - 16 t ^ { 2 }$ In how many seconds does the object reach its maximum height?

The graph of the function $g ( x )$ is a translation of the graph of $f ( x ) = x ^ { 2 }$ . Graph the function. $g ( x ) = ( x + 4 ) ^ { 2 } + 3$

Evaluate the difference quotient for the function. $f ( x ) = 4 x ^ { 2 } - 14$

The graph of the function $g ( x )$ is a translation of the graph of $f ( x ) = x ^ { 2 }$ . Graph the function. $g ( x ) = ( x + 1 ) ^ { 2 } + 3$

Graph the function. $f ( x ) = \frac { x ^ { 2 } - 2 x - 3 } { x ^ { 2 } - 3 x + 5 }$

At a time $t$ seconds after an object is tossed vertically upward, it reaches a height $s$ in feet given by the equation: $s = 128 t - 16 t ^ { 2 }$ In how many seconds does the object reach its maximum height?

Find the inverse of the one-to-one function. $y = 3 x + 9$

Graph the function. $y = [ [ 3 x ] ]$

A 330-room hotel is two-thirds filled when the nightly room rate is $70.Experience has shown that each $5 increase in cost results in 10 fewer occupied rooms.Find the nightly rate that will maximize Income.

Find the range of the function $f ( x ) = \frac { 4 x } { x - 5 }$ by finding the domain of $f ^ { - 1 } ( x )$ .

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

Determine whether the function is one-to-one. $y = \frac { 2 } { 9 } x$

Find the vertex of the parabola. $y = 2 x ^ { 2 } - 5$

A pizzeria charges $\$ 12.50$ plus $\$ 0.60$ per topping for a large pizza. Find the cost of a pizza that has 3 toppings.

A taxicab company charges $\$ 3$ for a trip up to 1 mile, and $\$ 2$ for every extra mile (or portion of a mile). Graph the ordered pairs $( m , c )$ , where $m$ represents the miles traveled and $c$ represents the cost.

Let $f ( x ) = 2 x - 1 , g ( x ) = 3 x - 2$ . Find the domain of the function. $( f \cdot g ) ( x )$

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

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Exam 4: Functions Functions and Function Notation

Graph the function. y=[[3x]]y = [ [ 3 x ] ]y=[[3x]]

Find the range of the function f(x)=4xx−2f ( x ) = \frac { 4 x } { x - 2 }f(x)=x−24x​ by finding the domain of f−1(x)f ^ { - 1 } ( x )f−1(x) .

A taxicab company charges $6\$ 6$6 for a trip up to 1 mile, and $5\$ 5$5 for every extra mile (or portion of a mile). Graph the ordered pairs (m,c)( m , c )(m,c) , where mmm represents the miles traveled and ccc represents the cost.

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−2)3−5g ( x ) = ( x - 2 ) ^ { 3 } - 5g(x)=(x−2)3−5

At a time t seconds after an object is tossed vertically upward, it reaches a height s in feet given by the equation: s=320t−16t2s = 320 t - 16 t ^ { 2 }s=320t−16t2 In how many seconds does the object reach its maximum height?

The graph of the function g(x)g ( x )g(x) is a translation of the graph of f(x)=x2f ( x ) = x ^ { 2 }f(x)=x2 . Graph the function. g(x)=(x+4)2+3g ( x ) = ( x + 4 ) ^ { 2 } + 3g(x)=(x+4)2+3

Evaluate the difference quotient for the function. f(x)=4x2−14f ( x ) = 4 x ^ { 2 } - 14f(x)=4x2−14

The graph of the function g(x)g ( x )g(x) is a translation of the graph of f(x)=x2f ( x ) = x ^ { 2 }f(x)=x2 . Graph the function. g(x)=(x+1)2+3g ( x ) = ( x + 1 ) ^ { 2 } + 3g(x)=(x+1)2+3

Graph the function. f(x)=x2−2x−3x2−3x+5f ( x ) = \frac { x ^ { 2 } - 2 x - 3 } { x ^ { 2 } - 3 x + 5 }f(x)=x2−3x+5x2−2x−3​

At a time ttt seconds after an object is tossed vertically upward, it reaches a height sss in feet given by the equation: s=128t−16t2s = 128 t - 16 t ^ { 2 }s=128t−16t2 In how many seconds does the object reach its maximum height?

Find the inverse of the one-to-one function. y=3x+9y = 3 x + 9y=3x+9

Graph the function. y=[[3x]]y = [ [ 3 x ] ]y=[[3x]]

A 330-room hotel is two-thirds filled when the nightly room rate is $70.Experience has shown that each $5 increase in cost results in 10 fewer occupied rooms.Find the nightly rate that will maximize Income.

Find the range of the function f(x)=4xx−5f ( x ) = \frac { 4 x } { x - 5 }f(x)=x−54x​ by finding the domain of f−1(x)f ^ { - 1 } ( x )f−1(x) .

Find the inverse of the one-to-one function. y=5xy = 5 xy=5x

Determine whether the function is one-to-one. y=29xy = \frac { 2 } { 9 } xy=92​x

Find the vertex of the parabola. y=2x2−5y = 2 x ^ { 2 } - 5y=2x2−5

A pizzeria charges $12.50\$ 12.50$12.50 plus $0.60\$ 0.60$0.60 per topping for a large pizza. Find the cost of a pizza that has 3 toppings.

A taxicab company charges $3\$ 3$3 for a trip up to 1 mile, and $2\$ 2$2 for every extra mile (or portion of a mile). Graph the ordered pairs (m,c)( m , c )(m,c) , where mmm represents the miles traveled and ccc represents the cost.

Let f(x)=2x−1,g(x)=3x−2f ( x ) = 2 x - 1 , g ( x ) = 3 x - 2f(x)=2x−1,g(x)=3x−2 . Find the domain of the function. (f⋅g)(x)( f \cdot g ) ( x )(f⋅g)(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

Graph the function. $y = [ [ 3 x ] ]$

Find the range of the function $f ( x ) = \frac { 4 x } { x - 2 }$ by finding the domain of $f ^ { - 1 } ( x )$ .

A taxicab company charges $\$ 6$ for a trip up to 1 mile, and $\$ 5$ for every extra mile (or portion of a mile). Graph the ordered pairs $( m , c )$ , where $m$ represents the miles traveled and $c$ represents the cost.

The graph of the function $g ( x )$ is a translation of the graph of $f ( x ) = x ^ { 3 }$ . Graph the function. $g ( x ) = ( x - 2 ) ^ { 3 } - 5$

At a time t seconds after an object is tossed vertically upward, it reaches a height s in feet given by the equation: $s = 320 t - 16 t ^ { 2 }$ In how many seconds does the object reach its maximum height?

The graph of the function $g ( x )$ is a translation of the graph of $f ( x ) = x ^ { 2 }$ . Graph the function. $g ( x ) = ( x + 4 ) ^ { 2 } + 3$

Evaluate the difference quotient for the function. $f ( x ) = 4 x ^ { 2 } - 14$

The graph of the function $g ( x )$ is a translation of the graph of $f ( x ) = x ^ { 2 }$ . Graph the function. $g ( x ) = ( x + 1 ) ^ { 2 } + 3$

Graph the function. $f ( x ) = \frac { x ^ { 2 } - 2 x - 3 } { x ^ { 2 } - 3 x + 5 }$

At a time $t$ seconds after an object is tossed vertically upward, it reaches a height $s$ in feet given by the equation: $s = 128 t - 16 t ^ { 2 }$ In how many seconds does the object reach its maximum height?

Find the inverse of the one-to-one function. $y = 3 x + 9$

Graph the function. $y = [ [ 3 x ] ]$

Find the range of the function $f ( x ) = \frac { 4 x } { x - 5 }$ by finding the domain of $f ^ { - 1 } ( x )$ .

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

Determine whether the function is one-to-one. $y = \frac { 2 } { 9 } x$

Find the vertex of the parabola. $y = 2 x ^ { 2 } - 5$

A pizzeria charges $\$ 12.50$ plus $\$ 0.60$ per topping for a large pizza. Find the cost of a pizza that has 3 toppings.

A taxicab company charges $\$ 3$ for a trip up to 1 mile, and $\$ 2$ for every extra mile (or portion of a mile). Graph the ordered pairs $( m , c )$ , where $m$ represents the miles traveled and $c$ represents the cost.

Let $f ( x ) = 2 x - 1 , g ( x ) = 3 x - 2$ . Find the domain of the function. $( f \cdot g ) ( x )$