Question 1

Determine whether $f ( x ) = x ^ { 2 } - x ^ { 6 }$ 
is even, odd, or neither.

Accepted Answer

Since $f ( x ) = f ( - x )$ , $f$ is even.

Question 2

Evaluate $f ( - 1 )$ , $f ( 0 )$
, $f ( 1 )$
, for the piecewise-defined function. $f ( x ) = \left\{ \begin{array} { l l } 
1 - 2 x & \text { if } x \leq 0 \
2 x - 1 & \text { if } x > 0
\end{array} \right.$

Accepted Answer

A)  $f ( - 1 ) = 3$
, $f ( 0 ) = - 1$
, $f ( 1 ) = 2$ 
B)  $f ( - 1 ) = 0$
, $f ( 0 ) = 3$
, $f ( 1 ) = - 3$ 
C)  $f ( - 1 ) = - 1$
, $f ( 0 ) = 0$
, $f ( 1 ) = 1$ 
D)  $f ( - 1 ) = - 1$
, $f (0 ) = 1$

, $f ( 1 ) = 1$ 
E)  none of these 
A)  $f ( - 1 ) = 3$
, $f ( 0 ) = - 1$
, $f ( 1 ) = 2$ 
B)  $f ( - 1 ) = 0$
, $f ( 0 ) = 3$
, $f ( 1 ) = - 3$ 
C)  $f ( - 1 ) = - 1$
, $f ( 0 ) = 0$
, $f ( 1 ) = 1$ 
D)  $f ( - 1 ) = - 1$
, $f (0 ) = 1$

, $f ( 1 ) = 1$ 
E)  none of these E

Question 3

Determine whether the curve represents a graph of a function.

Accepted Answer

A)  Function; the graph passes the horizontal line test 
B)  Function; the graph passes the vertical line test 
C)  Not a function; the graph passes the vertical line test 
D)  Not a function; the graph passes the horizontal line test 
E)  none 
A)  Function; the graph passes the horizontal line test 
B)  Function; the graph passes the vertical line test 
C)  Not a function; the graph passes the vertical line test 
D)  Not a function; the graph passes the horizontal line test 
E)  none B

Question 4

Graphs of the functions f and g are given
a) Which is larger, $f ( 0 ) \text { or } g ( 0 ) ?$ 
b) Which is larger, $$f ( - 1 ) \text { or } g ( - 1 ) ?$$ 
c)For which values of x is $$f ( x ) = g ( x ) ?$$

Accepted Answer

The answer of Graphs of the functions f and g...

Question 5

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

Accepted Answer

The answer of If \(f ( x ) = 3...

Question 6

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

Accepted Answer

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

Question 7

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

Accepted Answer

The answer of Determine whether the function in the figure...

Question 8

Use a graphing device to draw the graph of the function $f ( x ) = - 3 - 3 x ^ { 2 }$ . State approximately the interval(s) on which the function is increasing and on which the function is decreasing.

Accepted Answer

A)  $f$ is increasing on $( - \infty , 0 ]$ and decreasing on $[ 0 , \infty )$ 
B)  $f$ is increasing on $( - \infty , - 3 )$ and decreasing on $[ 3 , \infty )$ 
C)  $f$ is increasing on $( - \infty , \infty )$ 
D)  $f$ is and decreasing on $[ 0 , \infty )$ only 
E) none of these 
A)  $f$ is increasing on $( - \infty , 0 ]$ and decreasing on $[ 0 , \infty )$ 
B)  $f$ is increasing on $( - \infty , - 3 )$ and decreasing on $[ 3 , \infty )$ 
C)  $f$ is increasing on $( - \infty , \infty )$ 
D)  $f$ is and decreasing on $[ 0 , \infty )$ only 
E) none of these

Question 9

Use a graphing calculator to find, approximately the range of the function. $f ( x ) = x ^ { 4 } - x ^ { 3 } + 3 x ^ { 2 } + 2 x - 10$

Accepted Answer

A)  $[ 0 , \infty )$ 
B)  $( - \infty , \infty )$ 
C)  $[ - 10,10 )$ 
D)  $[ - \infty , 5 )$ 
E)  $[ - 10 , \infty )$ 
A)  $[ 0 , \infty )$ 
B)  $( - \infty , \infty )$ 
C)  $[ - 10,10 )$ 
D)  $[ - \infty , 5 )$ 
E)  $[ - 10 , \infty )$

Question 10

A function f is given, and the indicated transformations are applied to its graph (in the given order). Find the equation for the final transformed graph. $f ( x ) = \sqrt { x }$; shift 5 units to the left, stretch vertically by a factor of 2 , and reflect in the $x$-axis.

Accepted Answer

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

Question 11

Find the inverse of the function. $$g ( x ) = x ^ { 2 } - 9 , x \geq 0$$

Accepted Answer

A)  $g ^ { - 1 } ( x ) = - \sqrt { x + 9 }$ 
B)  $g ^ { - 1 } ( x ) = \sqrt { x + 9 }$ 
C)  $g ^ { - 1 } ( x ) = 9 + \sqrt { x }$ 
D)  $g ^ { - 1 } ( x ) = 9 - \sqrt { x }$ 
E)  none of these 
A)  $g ^ { - 1 } ( x ) = - \sqrt { x + 9 }$ 
B)  $g ^ { - 1 } ( x ) = \sqrt { x + 9 }$ 
C)  $g ^ { - 1 } ( x ) = 9 + \sqrt { x }$ 
D)  $g ^ { - 1 } ( x ) = 9 - \sqrt { x }$ 
E)  none of these

Question 12

Use a graphing calculator to find, approximately the range of the function. $f ( x ) = 2 x ^ { 4 } - x ^ { 3 } + x ^ { 2 } + 2 x - 7$

Accepted Answer

A)  $[ - 2,7 )$ 
B)  $( - \infty , \infty )$ 
C)  $[ - 14 , \infty )$ 
D)  $[ - 7 , \infty )$ 
E)  $[ - \infty , 7 )$ 
A)  $[ - 2,7 )$ 
B)  $( - \infty , \infty )$ 
C)  $[ - 14 , \infty )$ 
D)  $[ - 7 , \infty )$ 
E)  $[ - \infty , 7 )$

Question 13

Find the range of the function. $f ( x ) = - x ^ { 2 } - 2 x + 3$

Accepted Answer

The answer of Find the range of the function. \(f...

Question 14

A function is given. (a) Find all the local maximum and minimum values of the function and the value of x at which each occurs
b) Find the intervals on which the function is increasing and on which the function is decreasing. State each answer correct to two decimal places. $G ( x ) = \frac { 2 } { x ^ { 2 } + x + 1 }$

Accepted Answer

(a) local maximum @#LAT-DLM& w

Question 15

If $g ( x ) = 3 - \sqrt { 2 x - 6 }$, find $g ( 5 )$

Accepted Answer

A)  4 
B)  3 
C)  1 
D)  5 
E)  $3 - \sqrt { 10 }$ 
A)  4 
B)  3 
C)  1 
D)  5 
E)  $3 - \sqrt { 10 }$

Question 16

For the function $g ( t ) = \frac { 1 } { 3 t - 2 }$ 
determine the average rate of change between the values $t = 0$ 
and $t = a + 1$ 
.

Accepted Answer

Average ra

Question 17

Given $f ( x ) = 2 + x ^ { 2 }$ and $g ( x ) = \sqrt { x - 4 }$, find $( f \circ g ) ( 4 )$

Accepted Answer

A)  $( f \circ g ) ( 4 ) = 2$ 
B)  $( f \circ g ) ( 4 ) = 4$ 
C)  $( f \circ g ) ( 4 ) = - 2$ 
D)  $( f \circ g ) ( 4 ) = 0$ 
E)  $( f \circ g ) ( 4 ) = 1$ 
A)  $( f \circ g ) ( 4 ) = 2$ 
B)  $( f \circ g ) ( 4 ) = 4$ 
C)  $( f \circ g ) ( 4 ) = - 2$ 
D)  $( f \circ g ) ( 4 ) = 0$ 
E)  $( f \circ g ) ( 4 ) = 1$

Question 18

Find $f \circ g \circ h$
 , where $f ( x ) = \sqrt { 1 - x }$
, $g ( x ) = 1 - x ^ { 2 }$
, $h ( x ) = 1 + \sqrt { x }$

Accepted Answer

A)  $\sqrt { ( 1 + \sqrt { x } ) }$ 
B)  $1 + \sqrt { x }$ 
C)  $\sqrt { 1 + x ^ { 2 } }$ 
D)  $\sqrt { 1 - x }$ 
E)  $1 + x ^ { 2 }$ 
A)  $\sqrt { ( 1 + \sqrt { x } ) }$ 
B)  $1 + \sqrt { x }$ 
C)  $\sqrt { 1 + x ^ { 2 } }$ 
D)  $\sqrt { 1 - x }$ 
E)  $1 + x ^ { 2 }$

Question 19

Sketch the graph of the function. $$f ( x ) = \left\{ \begin{array} { l l c } 
- x & \text { if } \quad x  1
\end{array} \right.$$

Accepted Answer

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

Question 20

Find the inverse of the function. $g ( x ) = x ^ { 2 } - 16 , x \geq 0$

Accepted Answer

The answer of Find the inverse of the function. \(g...

Determine whether $f ( x ) = x ^ { 2 } - x ^ { 6 }$ is even, odd, or neither.

Evaluate $f ( - 1 )$ , $f ( 0 )$ , $f ( 1 )$ , for the piecewise-defined function. $f ( x ) = \left\{ \begin{array} { l l } 1 - 2 x & \text { if } x \leq 0 \\2 x - 1 & \text { if } x > 0\end{array} \right.$

Determine whether the curve represents a graph of a function.

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

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

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

Use a graphing device to draw the graph of the function $f ( x ) = - 3 - 3 x ^ { 2 }$ . State approximately the interval(s) on which the function is increasing and on which the function is decreasing.

Use a graphing calculator to find, approximately the range of the function. $f ( x ) = x ^ { 4 } - x ^ { 3 } + 3 x ^ { 2 } + 2 x - 10$

A function f is given, and the indicated transformations are applied to its graph (in the given order). Find the equation for the final transformed graph. $f ( x ) = \sqrt { x }$ ; shift 5 units to the left, stretch vertically by a factor of 2 , and reflect in the $x$ -axis.

Find the inverse of the function. $g ( x ) = x ^ { 2 } - 9 , x \geq 0$

Use a graphing calculator to find, approximately the range of the function. $f ( x ) = 2 x ^ { 4 } - x ^ { 3 } + x ^ { 2 } + 2 x - 7$

Find the range of the function. $f ( x ) = - x ^ { 2 } - 2 x + 3$

If $g ( x ) = 3 - \sqrt { 2 x - 6 }$ , find $g ( 5 )$

For the function $g ( t ) = \frac { 1 } { 3 t - 2 }$ determine the average rate of change between the values $t = 0$ and $t = a + 1$ .

Given $f ( x ) = 2 + x ^ { 2 }$ and $g ( x ) = \sqrt { x - 4 }$ , find $( f \circ g ) ( 4 )$

Find $f \circ g \circ h$ , where $f ( x ) = \sqrt { 1 - x }$ , $g ( x ) = 1 - x ^ { 2 }$ , $h ( x ) = 1 + \sqrt { x }$

Sketch the graph of the function. $f ( x ) = \left\{ \begin{array} { l l c } - x & \text { if } \quad x < - 1 \\x ^ { 2 } & \text { if } & - 1 \leq x \leq 1 \\1 & \text { if } & x > 1\end{array} \right.$

Find the inverse of the function. $g ( x ) = x ^ { 2 } - 16 , x \geq 0$

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 whether f(x)=x2−x6f ( x ) = x ^ { 2 } - x ^ { 6 }f(x)=x2−x6 is even, odd, or neither.

Determine whether the curve represents a graph of a function.

Graphs of the functions f and g are given a) Which is larger, f(0) or g(0)?f ( 0 ) \text { or } g ( 0 ) ?f(0) or g(0)? b) Which is larger, f(−1) or g(−1)?f ( - 1 ) \text { or } g ( - 1 ) ?f(−1) or g(−1)? c)For which values of x is f(x)=g(x)?f ( x ) = g ( x ) ?f(x)=g(x)?

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 (f∘g)(x)( f \circ g ) ( x )(f∘g)(x)

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)

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

Use a graphing device to draw the graph of the function f(x)=−3−3x2f ( x ) = - 3 - 3 x ^ { 2 }f(x)=−3−3x2 . State approximately the interval(s) on which the function is increasing and on which the function is decreasing.

Use a graphing calculator to find, approximately the range of the function. f(x)=x4−x3+3x2+2x−10f ( x ) = x ^ { 4 } - x ^ { 3 } + 3 x ^ { 2 } + 2 x - 10f(x)=x4−x3+3x2+2x−10

A function f is given, and the indicated transformations are applied to its graph (in the given order). Find the equation for the final transformed graph. f(x)=xf ( x ) = \sqrt { x }f(x)=x​ ; shift 5 units to the left, stretch vertically by a factor of 2 , and reflect in the xxx -axis.

Find the inverse of the function. g(x)=x2−9,x≥0g ( x ) = x ^ { 2 } - 9 , x \geq 0g(x)=x2−9,x≥0

Use a graphing calculator to find, approximately the range of the function. f(x)=2x4−x3+x2+2x−7f ( x ) = 2 x ^ { 4 } - x ^ { 3 } + x ^ { 2 } + 2 x - 7f(x)=2x4−x3+x2+2x−7

Find the range of the function. f(x)=−x2−2x+3f ( x ) = - x ^ { 2 } - 2 x + 3f(x)=−x2−2x+3

If g(x)=3−2x−6g ( x ) = 3 - \sqrt { 2 x - 6 }g(x)=3−2x−6​ , find g(5)g ( 5 )g(5)

For the function g(t)=13t−2g ( t ) = \frac { 1 } { 3 t - 2 }g(t)=3t−21​ determine the average rate of change between the values t=0t = 0t=0 and t=a+1t = a + 1t=a+1 .

Given f(x)=2+x2f ( x ) = 2 + x ^ { 2 }f(x)=2+x2 and g(x)=x−4g ( x ) = \sqrt { x - 4 }g(x)=x−4​ , find (f∘g)(4)( f \circ g ) ( 4 )(f∘g)(4)

Find f∘g∘hf \circ g \circ hf∘g∘h , where f(x)=1−xf ( x ) = \sqrt { 1 - x }f(x)=1−x​ , g(x)=1−x2g ( x ) = 1 - x ^ { 2 }g(x)=1−x2 , h(x)=1+xh ( x ) = 1 + \sqrt { x }h(x)=1+x​

Find the inverse of the function. g(x)=x2−16,x≥0g ( x ) = x ^ { 2 } - 16 , x \geq 0g(x)=x2−16,x≥0

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 whether $f ( x ) = x ^ { 2 } - x ^ { 6 }$ is even, odd, or neither.

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

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

Use a graphing device to draw the graph of the function $f ( x ) = - 3 - 3 x ^ { 2 }$ . State approximately the interval(s) on which the function is increasing and on which the function is decreasing.

Use a graphing calculator to find, approximately the range of the function. $f ( x ) = x ^ { 4 } - x ^ { 3 } + 3 x ^ { 2 } + 2 x - 10$

A function f is given, and the indicated transformations are applied to its graph (in the given order). Find the equation for the final transformed graph. $f ( x ) = \sqrt { x }$ ; shift 5 units to the left, stretch vertically by a factor of 2 , and reflect in the $x$ -axis.

Find the inverse of the function. $g ( x ) = x ^ { 2 } - 9 , x \geq 0$

Use a graphing calculator to find, approximately the range of the function. $f ( x ) = 2 x ^ { 4 } - x ^ { 3 } + x ^ { 2 } + 2 x - 7$

Find the range of the function. $f ( x ) = - x ^ { 2 } - 2 x + 3$

If $g ( x ) = 3 - \sqrt { 2 x - 6 }$ , find $g ( 5 )$

For the function $g ( t ) = \frac { 1 } { 3 t - 2 }$ determine the average rate of change between the values $t = 0$ and $t = a + 1$ .

Given $f ( x ) = 2 + x ^ { 2 }$ and $g ( x ) = \sqrt { x - 4 }$ , find $( f \circ g ) ( 4 )$

Find $f \circ g \circ h$ , where $f ( x ) = \sqrt { 1 - x }$ , $g ( x ) = 1 - x ^ { 2 }$ , $h ( x ) = 1 + \sqrt { x }$

Find the inverse of the function. $g ( x ) = x ^ { 2 } - 16 , x \geq 0$