Question 1

At a time $t$ seconds after an object is tossed vertically upward, it reaches a height $s$ in feet given by the equation:
$$s = 192 t - 16 t ^ { 2 }$$
In how many seconds does the object reach its maximum height?

Accepted Answer

A)  $\quad 6 \mathrm { sec }$ 
B)  $\quad 3 \mathrm { sec }$ 
C)  $288 \mathrm { sec }$ 
D)  $\quad 576 \mathrm { sec }$ 
E)  $\quad 12 \mathrm { sec }$

Question 2

Graph the function. $y = [ [ 2 x ] ]$

Accepted Answer

A) 
 
B) 
 
C) 
 
D)

Question 3

The function $f ( x ) = \sqrt { x ^ { 2 } - 6 }$ is one-to-one on the domain $x \leq - \sqrt { 6 }$. Find $f ^ { - 1 } ( x )$.

Accepted Answer

A)  $f ^ { - 1 } ( x ) = - \sqrt { x ^ { 2 } - 6 }$ 
B)  $\quad f ^ { - 1 } ( x ) = - \sqrt { x ^ { 2 } + 6 }$ 
C)  $f ^ { - 1 } ( x ) = x ^ { 2 } + 6$ 
D)  $f ^ { - 1 } ( x ) = \frac { 1 } { \sqrt { x ^ { 2 } - 6 } }$ 
E) 
$$f ^ { - 1 } ( x ) = \sqrt { x ^ { 2 } + 6 }$$

Question 4

Find the inverse of the one-to-one function. $$y = 2 x + 7$$

Accepted Answer

A)  $y = \frac { x + 7 } { 2 }$ 
B)  none of the above 
C)  $\quad y = \frac { 2 } { x - 7 }$ 
D)  $y = \frac { x - 2 } { 7 }$ 
E)  $y = \frac { x - 7 } { 2 }$

Question 5

Find the inverse of the one-to-one function. $$y = 8 x$$

Accepted Answer

A)  $\quad y = \frac { 8 } { x }$ 
B)  $\quad y = \frac { x } { 8 }$ 
C)  $\quad y = 64 x$ 
D)  $\quad y = 8 x ^ { 2 }$ 
E)  $y = 8 x$

Question 6

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

Accepted Answer

A) 
 
B) 
 
C) 
 
D)

Question 7

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 $A = \$ 28$ when $t = 1$ and $A = \$ 30$ when $t = 2$.

Accepted Answer

A)  $A = 2 t - 26$ 
B)  $A = - 2 t + 26$ 
C)  $\quad A = 30 t + 26$ 
D)  $A = 2 t + 26$ 
E)  $A = 30 t - 26$

Question 8

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

Question 9

The function $f ( x ) = \sqrt { x ^ { 2 } - 9 }$ is one-to-one on the domain $x \leq - \sqrt { 9 }$. Find $f ^ { - 1 } ( x )$.

Accepted Answer

A)  $\quad f ^ { - 1 } ( x ) = x ^ { 2 } + 9$ 
B)  $f ^ { - 1 } ( x ) = - \sqrt { x ^ { 2 } + 9 }$ 
C)  $f ^ { - 1 } ( x ) = \frac { 1 } { \sqrt { x ^ { 2 } - 9 } }$ 
D)  $\quad f ^ { - 1 } ( x ) = \sqrt { x ^ { 2 } + 9 }$ 
E)  $\quad f ^ { - 1 } ( x ) = - \sqrt { x ^ { 2 } - 9 }$

Question 10

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

Accepted Answer

A) 
 
B) 
 
C) 
 
D)

Question 11

Determine whether the function is one-to-one. $$y = \frac { 4 } { 7 } x$$

Accepted Answer

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

Question 12

Find the inverse of the one-to-one function. $y = 7 x$

Accepted Answer

A)  $\quad y = 7 x ^ { 2 }$ 
B)  $\quad y = 7 x$ 
C)  $\quad y = \frac { 7 } { x }$ 
D)  $\quad y = 49 x$ 
E)  $y = \frac { x } { 7 }$

Question 13

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

Accepted Answer

A) 
 
B) 
 
C) 
 
D)

Question 14

A pizzeria charges $8.50 plus $0.90 per topping for a large pizza.Find the cost of a pizza that has 5 toppings.

Accepted Answer

A)  $ \$ 13.00$ 
B)  $\$ 3.75$ 
C)  $\$ 14.35$ 
D)  $\$ 4.00$ 
E)  $\$ 14.00$

Question 15

A pizzeria charges $\$ 6.00$ plus $\$ 0.65$ per topping for a large pizza. Find the cost of a pizza that has 2 toppings.

Accepted Answer

A)  $\$ 4.45$ 
B)  $\$ 8.30$ 
C)  $\$ 4.70$ 
D)  $\quad \$ 8.65$ 
E)  $\$ 7.30$

Question 16

Find the vertex of the parabola. $y = 3 x ^ { 2 } - 2$

Accepted Answer

A)  $\quad ( - 2,0 )$ 
B)  $\quad ( - 2,3 )$ 
C)  $\quad ( 0,3 )$ 
D)  $\quad ( 3 , - 2 )$ 
E)  $\quad ( 0 , - 2 )$

Question 17

Find the vertex of the parabola. $$y = 2 x ^ { 2 } - 8$$

Accepted Answer

A)  $\quad ( - 8,0 )$ 
B)  $\quad ( 2 , - 8 )$ 
C)  $\quad ( - 8,2 )$ 
D)  $\quad ( 0 , - 8 )$ 
E)  $\quad ( 0,2 )$

Question 18

Graph the quadratic function. $f ( x ) = - x ^ { 2 } - 4 x + 5$

Accepted Answer

A) 
 
B) 
 
C) 
 
D)

Question 19

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

Accepted Answer

A) 
 
B) 
 
C)

$\mathrm { d }$.

Question 20

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

Accepted Answer

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

Exam 4: Functions Functions and Function Notation

At a time $t$ seconds after an object is tossed vertically upward, it reaches a height $s$ in feet given by the equation: $s = 192 t - 16 t ^ { 2 }$ In how many seconds does the object reach its maximum height?

Graph the function. $y = [ [ 2 x ] ]$

The function $f ( x ) = \sqrt { x ^ { 2 } - 6 }$ is one-to-one on the domain $x \leq - \sqrt { 6 }$ . Find $f ^ { - 1 } ( x )$ .

Find the inverse of the one-to-one function. $y = 2 x + 7$

Find the inverse of the one-to-one function. $y = 8 x$

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

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 $A = \$ 28$ when $t = 1$ and $A = \$ 30$ when $t = 2$ .

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

The function $f ( x ) = \sqrt { x ^ { 2 } - 9 }$ is one-to-one on the domain $x \leq - \sqrt { 9 }$ . Find $f ^ { - 1 } ( x )$ .

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

Determine whether the function is one-to-one. $y = \frac { 4 } { 7 } x$

Find the inverse of the one-to-one function. $y = 7 x$

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

A pizzeria charges $8.50 plus $0.90 per topping for a large pizza.Find the cost of a pizza that has 5 toppings.

A pizzeria charges $\$ 6.00$ plus $\$ 0.65$ per topping for a large pizza. Find the cost of a pizza that has 2 toppings.

Find the vertex of the parabola. $y = 3 x ^ { 2 } - 2$

Find the vertex of the parabola. $y = 2 x ^ { 2 } - 8$

Graph the quadratic function. $f ( x ) = - x ^ { 2 } - 4 x + 5$

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

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

Exam 4: Functions Functions and Function Notation

At a time ttt seconds after an object is tossed vertically upward, it reaches a height sss in feet given by the equation: s=192t−16t2s = 192 t - 16 t ^ { 2 }s=192t−16t2 In how many seconds does the object reach its maximum height?

Graph the function. y=[[2x]]y = [ [ 2 x ] ]y=[[2x]]

The function f(x) =x2−6f ( x ) = \sqrt { x ^ { 2 } - 6 }f(x) =x2−6​ is one-to-one on the domain x≤−6x \leq - \sqrt { 6 }x≤−6​ . Find f−1(x) f ^ { - 1 } ( x ) f−1(x) .

Find the inverse of the one-to-one function. y=2x+7y = 2 x + 7y=2x+7

Find the inverse of the one-to-one function. y=8xy = 8 xy=8x

Graph the rational function. f(x) =5x3+4x2xf ( x ) = \frac { 5 x ^ { 3 } + 4 x } { 2 x }f(x) =2x5x3+4x​ Note that the numerator and denominator of the fraction share a common factor.

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=$28A = \$ 28A=$28 when t=1t = 1t=1 and A=$30A = \$ 30A=$30 when t=2t = 2t=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)

The function f(x) =x2−9f ( x ) = \sqrt { x ^ { 2 } - 9 }f(x) =x2−9​ is one-to-one on the domain x≤−9x \leq - \sqrt { 9 }x≤−9​ . Find f−1(x) f ^ { - 1 } ( x ) f−1(x) .

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−1) 3−2g ( x ) = ( x - 1 ) ^ { 3 } - 2g(x) =(x−1) 3−2

Determine whether the function is one-to-one. y=47xy = \frac { 4 } { 7 } xy=74​x

Find the inverse of the one-to-one function. y=7xy = 7 xy=7x

Graph the rational function. f(x) =3x3+2x5xf ( x ) = \frac { 3 x ^ { 3 } + 2 x } { 5 x }f(x) =5x3x3+2x​ Note that the numerator and denominator of the fraction share a common factor.

A pizzeria charges $8.50 plus $0.90 per topping for a large pizza.Find the cost of a pizza that has 5 toppings.

A pizzeria charges $6.00\$ 6.00$6.00 plus $0.65\$ 0.65$0.65 per topping for a large pizza. Find the cost of a pizza that has 2 toppings.

Find the vertex of the parabola. y=3x2−2y = 3 x ^ { 2 } - 2y=3x2−2

Find the vertex of the parabola. y=2x2−8y = 2 x ^ { 2 } - 8y=2x2−8

Graph the quadratic function. f(x) =−x2−4x+5f ( x ) = - x ^ { 2 } - 4 x + 5f(x) =−x2−4x+5

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​

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 - g ) ( x ) (f−g) (x)

At a time $t$ seconds after an object is tossed vertically upward, it reaches a height $s$ in feet given by the equation: $s = 192 t - 16 t ^ { 2 }$ In how many seconds does the object reach its maximum height?

Graph the function. $y = [ [ 2 x ] ]$

The function $f ( x ) = \sqrt { x ^ { 2 } - 6 }$ is one-to-one on the domain $x \leq - \sqrt { 6 }$ . Find $f ^ { - 1 } ( x )$ .

Find the inverse of the one-to-one function. $y = 2 x + 7$

Find the inverse of the one-to-one function. $y = 8 x$

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

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 $A = \$ 28$ when $t = 1$ and $A = \$ 30$ when $t = 2$ .

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

The function $f ( x ) = \sqrt { x ^ { 2 } - 9 }$ is one-to-one on the domain $x \leq - \sqrt { 9 }$ . Find $f ^ { - 1 } ( x )$ .

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

Determine whether the function is one-to-one. $y = \frac { 4 } { 7 } x$

Find the inverse of the one-to-one function. $y = 7 x$

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

A pizzeria charges $\$ 6.00$ plus $\$ 0.65$ per topping for a large pizza. Find the cost of a pizza that has 2 toppings.

Find the vertex of the parabola. $y = 3 x ^ { 2 } - 2$

Find the vertex of the parabola. $y = 2 x ^ { 2 } - 8$

Graph the quadratic function. $f ( x ) = - x ^ { 2 } - 4 x + 5$

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

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