Question 1

Determine if the equation $x ^ { 2 } + y ^ { 2 } = 49$ defines y as a function of x

Accepted Answer

A)  The equation represents a function because it's a circle 
B)  The equation represents a function because for each value of x there is always two values of y 
C)  Not a function because the equation gives two values of y for a given value of x 
D)  The equation represents a function because it passes the vertical line test 
E)  Not a function because the equation passes the vertical line test. 
A)  The equation represents a function because it's a circle 
B)  The equation represents a function because for each value of x there is always two values of y 
C)  Not a function because the equation gives two values of y for a given value of x 
D)  The equation represents a function because it passes the vertical line test 
E)  Not a function because the equation passes the vertical line test.

Question 2

Determine whether the function in the figure is even, odd, or neither.

Accepted Answer

A)  even 
B)  odd 
C)  neither even or odd 
D)  both even and odd 
A)  even 
B)  odd 
C)  neither even or odd 
D)  both even and odd

Question 3

$\text { If } f ( x ) = ( x - 2 ) ^ { 2 } + 5 , \text { find } f ( 2 ) , f ( a ) , \text { and } f ( 1 / a )$

Accepted Answer

\[\begin{array} { l } 
f ( 2 ) = ( 2 - 2

Question 4

Use a graphing calculator or computer to determine whether the function $f ( x ) = - | x | - | 5 - x |$ 
is one-to-one.

Accepted Answer

Using a graphing cal

Question 5

For the function $f ( t ) = \frac { 1 } { t }$ determine the average rate of change between the values $t = \tau$ And $t = a + h$

Accepted Answer

A)  $\frac { - 1 } { a ( a + h ) }$ 
B)  $\frac { - 2 } { h }$ 
C)  $( 3 h + 1 )$ 
D)  $\frac { - 1 } { ( 2 h - 1 ) }$ 
E)  $\frac { 1 } { a ( a + h ) }$ 
A)  $\frac { - 1 } { a ( a + h ) }$ 
B)  $\frac { - 2 } { h }$ 
C)  $( 3 h + 1 )$ 
D)  $\frac { - 1 } { ( 2 h - 1 ) }$ 
E)  $\frac { 1 } { a ( a + h ) }$

Question 6

Find the inverse of the function. $f ( x ) = 3 x + 2$

Accepted Answer

A)  $f ^ { - 1 } ( x ) = x - 2$ 
B)  $f ^ { - 1 } ( x ) = 2 x$ 
C)  $f ^ { - 1 } ( x ) = \frac { x + 2 } { 3 }$ 
D)  $f ^ { - 1 } ( x ) = \frac { x - 2 } { 3 }$ 
E)  none of these 
A)  $f ^ { - 1 } ( x ) = x - 2$ 
B)  $f ^ { - 1 } ( x ) = 2 x$ 
C)  $f ^ { - 1 } ( x ) = \frac { x + 2 } { 3 }$ 
D)  $f ^ { - 1 } ( x ) = \frac { x - 2 } { 3 }$ 
E)  none of these

Question 7

Given $f ( x ) = 2 + x ^ { 2 }$ 
and $g ( x ) = \sqrt { x - 1 }$ 
, find $( f \circ g ) ( 2 )$ 
, $( f \circ f ) ( 2 )$ 
.

Accepted Answer

The answer of Given \(f ( x ) = 2...

Question 8

If $f ( x ) = 3 x - 2$ and $g ( x ) = 3 + 2 x ^ { 2 }$, find $f g$ and $( g \circ f ) ( x )$

Accepted Answer

A)  $f g = x ^ { 3 } - 4 x ^ { 2 } + 9 x - 1 ; \quad \quad ( g \circ f ) ( x ) = 18 x ^ { 2 } - 24 x + 11$ 
B)  $f g = 6 x ^ { 3 } - 4 x ^ { 2 } + 9 x - 6 ; \quad  (g \circ f ) ( x ) = 18 x ^ { 2 } - 24 x + 11$ 
C)  $f g = 2 x ^ { 2 } + 3 x + 1$; $\quad $ $\quad $ $\quad $$( g \circ f ) ( x ) = 6 x ^ { 2 } + 7$ 
D)  $f g = 6 x ^ { 2 } + 7$; $\quad $ $\quad $ $\quad $ $\quad $$( g \circ f ) ( x ) = 6 x ^ { 3 } - 4 x ^ { 2 } + 9 x - 6$ 
E)  none of these 
A)  $f g = x ^ { 3 } - 4 x ^ { 2 } + 9 x - 1 ; \quad \quad ( g \circ f ) ( x ) = 18 x ^ { 2 } - 24 x + 11$ 
B)  $f g = 6 x ^ { 3 } - 4 x ^ { 2 } + 9 x - 6 ; \quad  (g \circ f ) ( x ) = 18 x ^ { 2 } - 24 x + 11$ 
C)  $f g = 2 x ^ { 2 } + 3 x + 1$; $\quad $ $\quad $ $\quad $$( g \circ f ) ( x ) = 6 x ^ { 2 } + 7$ 
D)  $f g = 6 x ^ { 2 } + 7$; $\quad $ $\quad $ $\quad $ $\quad $$( g \circ f ) ( x ) = 6 x ^ { 3 } - 4 x ^ { 2 } + 9 x - 6$ 
E)  none of these

Question 9

Sketch the graph of the function. $h ( x ) = \frac { 1 } { ( x - 2 ) ^ { 2 } }$

Accepted Answer

The answer of Sketch the graph of the function. \(h...

Question 10

Draw the graph of the function in an appropriate viewing rectangle. $f ( x ) = 1.1 x ^ { 3 } - 8.6 x ^ { 2 } - 1.4 x + 1.2$

Accepted Answer

The answer of Draw the graph of the function in...

Question 11

Determine which viewing rectangle produces the most appropriate graph of the function. $$g ( x ) = 6 x ^ { 3 } - 15 x ^ { 2 } + 4 x - 1$$

Accepted Answer

A)  $[ - 2,2 ]$ by $[ - 2,2 ]$ 
B)  $[ - 8,8 ]$ by $[ - 8,8 ]$ 
C)  $[ - 4,4 ]$ by $[ - 12,12 ]$ 
D)  $[ - 100,100 ]$ by $[ - 100,100 ]$ 
E)  $[ - 10,10 ]$ by $[ - 100,100 ]$ 
A)  $[ - 2,2 ]$ by $[ - 2,2 ]$ 
B)  $[ - 8,8 ]$ by $[ - 8,8 ]$ 
C)  $[ - 4,4 ]$ by $[ - 12,12 ]$ 
D)  $[ - 100,100 ]$ by $[ - 100,100 ]$ 
E)  $[ - 10,10 ]$ by $[ - 100,100 ]$

Question 12

Find the inverse of the function. $f ( x ) = \frac { x - 7 } { 4 }$

Accepted Answer

A)  $f ^ { - 1 } ( x ) = x + 7$ 
B)  $f ^ { - 1 } ( x ) = \frac { 4 x } { 7 }$ 
C)  $f ^ { - 1 } ( x ) = \frac { x + 7 } { 4 }$ 
D)  $f ^ { - 1 } ( x ) = 4 x + 7$ 
E)  none of these 
A)  $f ^ { - 1 } ( x ) = x + 7$ 
B)  $f ^ { - 1 } ( x ) = \frac { 4 x } { 7 }$ 
C)  $f ^ { - 1 } ( x ) = \frac { x + 7 } { 4 }$ 
D)  $f ^ { - 1 } ( x ) = 4 x + 7$ 
E)  none of these

Question 13

The graph of a function h is given
a) Find $h ( - 3 ) , h ( - 2 ) , h ( 0 ) , \text { and } h ( 3 )$ 
b) Find the domain and range of h
c) Find the values of x for which $h ( x ) = 3$ 
d) Find the values of x for which $h ( x ) \leq 3$

Accepted Answer

(a) @#LAT-DLM&

b)

Question 14

Given $f ( x ) = 1 - x ^ { 2 }$ and $g ( x ) = \sqrt { x - 1 }$
, find $( f \circ g ) ( 5 )$

Accepted Answer

A)  $( f \circ g ) ( 5 ) = - 2$ 
B)  $( f \circ g ) ( 5 ) = 5$ 
C)  $( f \circ g ) ( 5 ) = - 3$ 
D)  $( f \circ g ) ( 5 ) = 1$ 
E)  $( f \circ g ) ( 5 ) = - 1$ 
A)  $( f \circ g ) ( 5 ) = - 2$ 
B)  $( f \circ g ) ( 5 ) = 5$ 
C)  $( f \circ g ) ( 5 ) = - 3$ 
D)  $( f \circ g ) ( 5 ) = 1$ 
E)  $( f \circ g ) ( 5 ) = - 1$

Question 15

Sketch the graph of the function  $h ( x ) = 3 - 8 x - 2 x ^ { 2 }$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
E)  none 
A) 
  
B) 
  
C) 
  
D) 
  
E)  none

Question 16

Use a graphing calculator to estimate the range of the function. $f ( x ) = x ^ { 4 } - x ^ { 3 } + x ^ { 2 } + 2 x - 15$

Accepted Answer

The answer of Use a graphing calculator to estimate the...

Question 17

Find the average rate of change of the function $f$ between the points given. $f ( x ) = \frac { 1 } { x - 3 } ; x = 2 , x = 7$

Accepted Answer

A)  $1 / 4$ 
B)  $1 / 5$ 
C)  $- 1 / 5$ 
D)  $- 4$ 
E)  $- 1$ 
A)  $1 / 4$ 
B)  $1 / 5$ 
C)  $- 1 / 5$ 
D)  $- 4$ 
E)  $- 1$

Question 18

Sketch the graph of the function. $$h ( x ) = x ^ { 3 } - 4 x ^ { 2 }$$

Accepted Answer

The answer of Sketch the graph of the function. \[h...

Question 19

Use a graphing calculator to determine approximately the intervals on which the function is increasing, and on which $f$ is decreasing. $f ( x ) = x ^ { 4 } + 6 x ^ { 3 } + x ^ { 2 } - 24 x + 16$

Accepted Answer

The function is incr

Question 20

Use a graphing calculator to determine approximately the intervals on which the function is increasing, and on which $f$ 
is decreasing. $f ( x ) = x ^ { 4 } + 6 x ^ { 3 } + x ^ { 2 } - 24 x + 16$

Accepted Answer

The function is incr

Determine if the equation $x ^ { 2 } + y ^ { 2 } = 49$ defines y as a function of x

Determine whether the function in the figure is even, odd, or neither.

$\text { If } f ( x ) = ( x - 2 ) ^ { 2 } + 5 , \text { find } f ( 2 ) , f ( a ) , \text { and } f ( 1 / a )$

Use a graphing calculator or computer to determine whether the function $f ( x ) = - | x | - | 5 - x |$ is one-to-one.

For the function $f ( t ) = \frac { 1 } { t }$ determine the average rate of change between the values $t = \tau$ And $t = a + h$

Find the inverse of the function. $f ( x ) = 3 x + 2$

Given $f ( x ) = 2 + x ^ { 2 }$ and $g ( x ) = \sqrt { x - 1 }$ , find $( f \circ g ) ( 2 )$ , $( f \circ f ) ( 2 )$ .

If $f ( x ) = 3 x - 2$ and $g ( x ) = 3 + 2 x ^ { 2 }$ , find $f g$ and $( g \circ f ) ( x )$

Sketch the graph of the function. $h ( x ) = \frac { 1 } { ( x - 2 ) ^ { 2 } }$

Draw the graph of the function in an appropriate viewing rectangle. $f ( x ) = 1.1 x ^ { 3 } - 8.6 x ^ { 2 } - 1.4 x + 1.2$

Determine which viewing rectangle produces the most appropriate graph of the function. $g ( x ) = 6 x ^ { 3 } - 15 x ^ { 2 } + 4 x - 1$

Find the inverse of the function. $f ( x ) = \frac { x - 7 } { 4 }$

Given $f ( x ) = 1 - x ^ { 2 }$ and $g ( x ) = \sqrt { x - 1 }$ , find $( f \circ g ) ( 5 )$

Sketch the graph of the function $h ( x ) = 3 - 8 x - 2 x ^ { 2 }$

Use a graphing calculator to estimate the range of the function. $f ( x ) = x ^ { 4 } - x ^ { 3 } + x ^ { 2 } + 2 x - 15$

Find the average rate of change of the function $f$ between the points given. $f ( x ) = \frac { 1 } { x - 3 } ; x = 2 , x = 7$

Sketch the graph of the function. $h ( x ) = x ^ { 3 } - 4 x ^ { 2 }$

Use a graphing calculator to determine approximately the intervals on which the function is increasing, and on which $f$ is decreasing. $f ( x ) = x ^ { 4 } + 6 x ^ { 3 } + x ^ { 2 } - 24 x + 16$

Use a graphing calculator to determine approximately the intervals on which the function is increasing, and on which $f$ is decreasing. $f ( x ) = x ^ { 4 } + 6 x ^ { 3 } + x ^ { 2 } - 24 x + 16$

Equations and Graphs

Functions

Exponential and Logarithmic Functions

Trigonometric Functions: Right Triangle Approach

Trigonometric Functions: Unit Circle Approach

Conic Sections

Polar Coordinates and Parametric Equations

Vectors in Two and Three Dimensions

Systems of Equations and Inequalities

Matrices and Determinants

Conic Sections

Sequences and Series

Counting and Probability

Filters

Exam 3: Polynomial and Rational Functions

Determine if the equation x2+y2=49x ^ { 2 } + y ^ { 2 } = 49x2+y2=49 defines y as a function of x

Determine whether the function in the figure is even, odd, or neither.

If f(x)=(x−2)2+5, find f(2),f(a), and f(1/a)\text { If } f ( x ) = ( x - 2 ) ^ { 2 } + 5 , \text { find } f ( 2 ) , f ( a ) , \text { and } f ( 1 / a ) If f(x)=(x−2)2+5, find f(2),f(a), and f(1/a)

Use a graphing calculator or computer to determine whether the function f(x)=−∣x∣−∣5−x∣f ( x ) = - | x | - | 5 - x |f(x)=−∣x∣−∣5−x∣ is one-to-one.

For the function f(t)=1tf ( t ) = \frac { 1 } { t }f(t)=t1​ determine the average rate of change between the values t=τt = \taut=τ And t=a+ht = a + ht=a+h

Find the inverse of the function. f(x)=3x+2f ( x ) = 3 x + 2f(x)=3x+2

Given f(x)=2+x2f ( x ) = 2 + x ^ { 2 }f(x)=2+x2 and g(x)=x−1g ( x ) = \sqrt { x - 1 }g(x)=x−1​ , find (f∘g)(2)( f \circ g ) ( 2 )(f∘g)(2) , (f∘f)(2)( f \circ f ) ( 2 )(f∘f)(2) .

If f(x)=3x−2f ( x ) = 3 x - 2f(x)=3x−2 and g(x)=3+2x2g ( x ) = 3 + 2 x ^ { 2 }g(x)=3+2x2 , find fgf gfg and (g∘f)(x)( g \circ f ) ( x )(g∘f)(x)

Sketch the graph of the function. h(x)=1(x−2)2h ( x ) = \frac { 1 } { ( x - 2 ) ^ { 2 } }h(x)=(x−2)21​

Draw the graph of the function in an appropriate viewing rectangle. f(x)=1.1x3−8.6x2−1.4x+1.2f ( x ) = 1.1 x ^ { 3 } - 8.6 x ^ { 2 } - 1.4 x + 1.2f(x)=1.1x3−8.6x2−1.4x+1.2

Determine which viewing rectangle produces the most appropriate graph of the function. g(x)=6x3−15x2+4x−1g ( x ) = 6 x ^ { 3 } - 15 x ^ { 2 } + 4 x - 1g(x)=6x3−15x2+4x−1

Find the inverse of the function. f(x)=x−74f ( x ) = \frac { x - 7 } { 4 }f(x)=4x−7​

Given f(x)=1−x2f ( x ) = 1 - x ^ { 2 }f(x)=1−x2 and g(x)=x−1g ( x ) = \sqrt { x - 1 }g(x)=x−1​ , find (f∘g)(5)( f \circ g ) ( 5 )(f∘g)(5)

Sketch the graph of the function h(x)=3−8x−2x2h ( x ) = 3 - 8 x - 2 x ^ { 2 }h(x)=3−8x−2x2

Use a graphing calculator to estimate the range of the function. f(x)=x4−x3+x2+2x−15f ( x ) = x ^ { 4 } - x ^ { 3 } + x ^ { 2 } + 2 x - 15f(x)=x4−x3+x2+2x−15

Find the average rate of change of the function fff between the points given. f(x)=1x−3;x=2,x=7f ( x ) = \frac { 1 } { x - 3 } ; x = 2 , x = 7f(x)=x−31​;x=2,x=7

Sketch the graph of the function. h(x)=x3−4x2h ( x ) = x ^ { 3 } - 4 x ^ { 2 }h(x)=x3−4x2

Use a graphing calculator to determine approximately the intervals on which the function is increasing, and on which fff is decreasing. f(x)=x4+6x3+x2−24x+16f ( x ) = x ^ { 4 } + 6 x ^ { 3 } + x ^ { 2 } - 24 x + 16f(x)=x4+6x3+x2−24x+16

Use a graphing calculator to determine approximately the intervals on which the function is increasing, and on which fff is decreasing. f(x)=x4+6x3+x2−24x+16f ( x ) = x ^ { 4 } + 6 x ^ { 3 } + x ^ { 2 } - 24 x + 16f(x)=x4+6x3+x2−24x+16

Equations and Graphs

Functions

Exponential and Logarithmic Functions

Trigonometric Functions: Right Triangle Approach

Trigonometric Functions: Unit Circle Approach

Conic Sections

Polar Coordinates and Parametric Equations

Vectors in Two and Three Dimensions

Systems of Equations and Inequalities

Matrices and Determinants

Conic Sections

Sequences and Series

Counting and Probability

Filters

Determine if the equation $x ^ { 2 } + y ^ { 2 } = 49$ defines y as a function of x

$\text { If } f ( x ) = ( x - 2 ) ^ { 2 } + 5 , \text { find } f ( 2 ) , f ( a ) , \text { and } f ( 1 / a )$

Use a graphing calculator or computer to determine whether the function $f ( x ) = - | x | - | 5 - x |$ is one-to-one.

For the function $f ( t ) = \frac { 1 } { t }$ determine the average rate of change between the values $t = \tau$ And $t = a + h$

Find the inverse of the function. $f ( x ) = 3 x + 2$

Given $f ( x ) = 2 + x ^ { 2 }$ and $g ( x ) = \sqrt { x - 1 }$ , find $( f \circ g ) ( 2 )$ , $( f \circ f ) ( 2 )$ .

If $f ( x ) = 3 x - 2$ and $g ( x ) = 3 + 2 x ^ { 2 }$ , find $f g$ and $( g \circ f ) ( x )$

Sketch the graph of the function. $h ( x ) = \frac { 1 } { ( x - 2 ) ^ { 2 } }$

Draw the graph of the function in an appropriate viewing rectangle. $f ( x ) = 1.1 x ^ { 3 } - 8.6 x ^ { 2 } - 1.4 x + 1.2$

Determine which viewing rectangle produces the most appropriate graph of the function. $g ( x ) = 6 x ^ { 3 } - 15 x ^ { 2 } + 4 x - 1$

Find the inverse of the function. $f ( x ) = \frac { x - 7 } { 4 }$

Given $f ( x ) = 1 - x ^ { 2 }$ and $g ( x ) = \sqrt { x - 1 }$ , find $( f \circ g ) ( 5 )$

Sketch the graph of the function $h ( x ) = 3 - 8 x - 2 x ^ { 2 }$

Use a graphing calculator to estimate the range of the function. $f ( x ) = x ^ { 4 } - x ^ { 3 } + x ^ { 2 } + 2 x - 15$

Find the average rate of change of the function $f$ between the points given. $f ( x ) = \frac { 1 } { x - 3 } ; x = 2 , x = 7$

Sketch the graph of the function. $h ( x ) = x ^ { 3 } - 4 x ^ { 2 }$

Use a graphing calculator to determine approximately the intervals on which the function is increasing, and on which $f$ is decreasing. $f ( x ) = x ^ { 4 } + 6 x ^ { 3 } + x ^ { 2 } - 24 x + 16$

Use a graphing calculator to determine approximately the intervals on which the function is increasing, and on which $f$ is decreasing. $f ( x ) = x ^ { 4 } + 6 x ^ { 3 } + x ^ { 2 } - 24 x + 16$