Question 1

The graph of $f ( x ) = | x | - 3$ is shown. Use this graph to sketch the graph of $g ( x ) = | | x | - 3 |$ .

Accepted Answer

The values of @#LAT-DLM& betwe

Question 2

For the function $f ( x ) = \frac { 2 } { 3 } x ^ { 4 } - \frac { 1 } { 3 } x ^ { 5 } - x + 3$ determine the average rate of change between the values $x = - 1$ and $x = 1 .$

Accepted Answer

The answer of For the function \(f ( x )...

Question 3

Sketch the graph of the piecewise-defined function. $$f ( x ) = \left\{ \begin{array} { l l } 
x + 2 & \text { if } x < 0 \
2 & \text { if } 0 \leq x \leq 1 \
- x + 6 & \text { if } 1 < x
\end{array} \right.$$

Accepted Answer

The answer of Sketch the graph of the piecewise-defined function....

Question 4

Determine whether or not the function $h ( x ) = 3 x ^ { 6 } + 2$ , $0 \leq x \leq \infty$ is one-to-one.

Accepted Answer

If @#LAT-DLM& then @#LAT-DLM& because di

Question 5

Use a graphing device to the graph of the function $f ( x ) = x ^ { 4 } + 2 x ^ { 3 } - 3 x ^ { 2 } - 4 x + 4$ . State approximately the intervals on which the function is increasing and on which the function is decreasing.

Accepted Answer

@#LAT-DLM& is increasing on @#LAT-DLM& a

Question 6

Find the domain of the function $h ( x ) = \sqrt { 2 x ^ { 2 } + 3 x + 1 }$ .

Accepted Answer

We need the radicand to be non

Question 7

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 8

Determine whether or not the function given by the graph is one-to-one.

Accepted Answer

No, it fai

Question 9

The graph of a function is given. Determine the average rate of change of the function between the indicated points on the graph.
 (2,8) $( - 2 , - 8 )$

Accepted Answer

The average rate of

Question 10

Evaluate $f ( - 2 )$ , $f ( - 1 )$ , $f ( 0 )$ , $f ( 1 )$ , and $f ( 5 )$ for the piecewise-defined function. $f ( x ) = \left\{ \begin{array} { l l } 
3 x ^ { 2 } & \text { if } x < 0 \
2 x + 1 & \text { if } x \geq 0
\end{array} \right.$

Accepted Answer

The answer of Evaluate $f ( - 2 )$ ,...

Question 11

Express the function $H ( x ) = \left( 2 + x ^ { 2 } \right) ^ { 3 }$ in the form $f \circ g$ .

Accepted Answer

The answer of Express the function \(H ( x )...

Question 12

Let $f ( x ) = x ^ { 3 } + c$ . Graph the family of functions with $c = - 4$ , $- 2$ , $0$ , $2$ , and $4$ in the viewing rectangle $[ - 5,5 ]$ by $[ - 5,5 ]$ . How does the value of $c$ affect the graph?

Accepted Answer

For values @#LAT-DLM& , the gr

Question 13

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 all answers correct to two decimal places.
 $U ( x ) = 2 \left( x ^ { 3 } - x \right)$

Accepted Answer

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

Question 14

Use $f ( x ) = x - 4$ and $g ( x ) = 2 - x ^ { 2 }$ to evaluate the expression $g ( g ( 1 ) )$ .

Accepted Answer

A)  $1$ 
B)  $3$ 
C)  $- 1$ 
D)  $- 3$ 
E)  $0$ 
A)  $1$ 
B)  $3$ 
C)  $- 1$ 
D)  $- 3$ 
E)  $0$

Question 15

Determine whether or not the function given by the graph is one-to-one.

Accepted Answer

Yes, it pa

Question 16

The graph of a function h is given.
(a) Find $h ( - 3 ) , h ( - 2 ) , h ( 2 ) , \text { and } h ( 4 )$
(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) @#LAT-DLM&

Question 17

Determine if the equation $x ^ { 2 } + y ^ { 2 } - 25 = 0$ defines $y$ as a function of $x$ . Explain your answer.

Accepted Answer

@#LAT-DLM& @#LAT-DLM& @#LAT-DLM& @#LAT-DLM& @#LAT-DLM& . No. This equa

Question 18

Determine whether or not the function $g ( x ) = | 2 x - 4 |$ is one-to-one.

Accepted Answer

@#LAT-DLM& , so @#LAT-DLM& is

Question 19

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

Accepted Answer

@#LAT-DLM& is increa

Question 20

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 all answers correct to two decimal places.
 $U ( x ) = 4 \left( x ^ { 3 } - x \right)$

Accepted Answer

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

The graph of $f ( x ) = | x | - 3$ is shown. Use this graph to sketch the graph of $g ( x ) = | | x | - 3 |$ .

For the function $f ( x ) = \frac { 2 } { 3 } x ^ { 4 } - \frac { 1 } { 3 } x ^ { 5 } - x + 3$ determine the average rate of change between the values $x = - 1$ and $x = 1 .$

Sketch the graph of the piecewise-defined function. $f ( x ) = \left\{ \begin{array} { l l } x + 2 & \text { if } x < 0 \\2 & \text { if } 0 \leq x \leq 1 \\- x + 6 & \text { if } 1 < x\end{array} \right.$

Determine whether or not the function $h ( x ) = 3 x ^ { 6 } + 2$ , $0 \leq x \leq \infty$ is one-to-one.

Use a graphing device to the graph of the function $f ( x ) = x ^ { 4 } + 2 x ^ { 3 } - 3 x ^ { 2 } - 4 x + 4$ . State approximately the intervals on which the function is increasing and on which the function is decreasing.

Find the domain of the function $h ( x ) = \sqrt { 2 x ^ { 2 } + 3 x + 1 }$ .

Determine whether or not the function given by the graph is one-to-one.

The graph of a function is given. Determine the average rate of change of the function between the indicated points on the graph. (2,8) $( - 2 , - 8 )$

Evaluate $f ( - 2 )$ , $f ( - 1 )$ , $f ( 0 )$ , $f ( 1 )$ , and $f ( 5 )$ for the piecewise-defined function. $f ( x ) = \left\{ \begin{array} { l l } 3 x ^ { 2 } & \text { if } x < 0 \\2 x + 1 & \text { if } x \geq 0\end{array} \right.$

Express the function $H ( x ) = \left( 2 + x ^ { 2 } \right) ^ { 3 }$ in the form $f \circ g$ .

Let $f ( x ) = x ^ { 3 } + c$ . Graph the family of functions with $c = - 4$ , $- 2$ , $0$ , $2$ , and $4$ in the viewing rectangle $[ - 5,5 ]$ by $[ - 5,5 ]$ . How does the value of $c$ affect the graph?

Use $f ( x ) = x - 4$ and $g ( x ) = 2 - x ^ { 2 }$ to evaluate the expression $g ( g ( 1 ) )$ .

Determine whether or not the function given by the graph is one-to-one.

Determine if the equation $x ^ { 2 } + y ^ { 2 } - 25 = 0$ defines $y$ as a function of $x$ . Explain your answer.

Determine whether or not the function $g ( x ) = | 2 x - 4 |$ is one-to-one.

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

Fundamentals

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions: Unit Circle Approach

Trigonometric Functions: Right Triangle Approach

Analytic Trigonometry

Polar Coordinates and Parametric Equations

Vectors in Two and Three Dimensions

Systems of Equations and Inequalities

Conic Sections

Sequences and Series

Limits: a Preview of Calculus

Filters

Exam 2: Functions

The graph of f(x)=∣x∣−3f ( x ) = | x | - 3f(x)=∣x∣−3 is shown. Use this graph to sketch the graph of g(x)=∣∣x∣−3∣g ( x ) = | | x | - 3 |g(x)=∣∣x∣−3∣ .

For the function f(x)=23x4−13x5−x+3f ( x ) = \frac { 2 } { 3 } x ^ { 4 } - \frac { 1 } { 3 } x ^ { 5 } - x + 3f(x)=32​x4−31​x5−x+3 determine the average rate of change between the values x=−1x = - 1x=−1 and x=1.x = 1 .x=1.

Determine whether or not the function h(x)=3x6+2h ( x ) = 3 x ^ { 6 } + 2h(x)=3x6+2 , 0≤x≤∞0 \leq x \leq \infty0≤x≤∞ is one-to-one.

Use a graphing device to the graph of the function f(x)=x4+2x3−3x2−4x+4f ( x ) = x ^ { 4 } + 2 x ^ { 3 } - 3 x ^ { 2 } - 4 x + 4f(x)=x4+2x3−3x2−4x+4 . State approximately the intervals on which the function is increasing and on which the function is decreasing.

Find the domain of the function h(x)=2x2+3x+1h ( x ) = \sqrt { 2 x ^ { 2 } + 3 x + 1 }h(x)=2x2+3x+1​ .

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)?

Determine whether or not the function given by the graph is one-to-one.

The graph of a function is given. Determine the average rate of change of the function between the indicated points on the graph. (2,8) (−2,−8)( - 2 , - 8 )(−2,−8)

Express the function H(x)=(2+x2)3H ( x ) = \left( 2 + x ^ { 2 } \right) ^ { 3 }H(x)=(2+x2)3 in the form f∘gf \circ gf∘g .

Let f(x)=x3+cf ( x ) = x ^ { 3 } + cf(x)=x3+c . Graph the family of functions with c=−4c = - 4c=−4 , −2- 2−2 , 000 , 222 , and 444 in the viewing rectangle [−5,5][ - 5,5 ][−5,5] by [−5,5][ - 5,5 ][−5,5] . How does the value of ccc affect the graph?

Use f(x)=x−4f ( x ) = x - 4f(x)=x−4 and g(x)=2−x2g ( x ) = 2 - x ^ { 2 }g(x)=2−x2 to evaluate the expression g(g(1))g ( g ( 1 ) )g(g(1)) .

Determine whether or not the function given by the graph is one-to-one.

Determine if the equation x2+y2−25=0x ^ { 2 } + y ^ { 2 } - 25 = 0x2+y2−25=0 defines yyy as a function of xxx . Explain your answer.

Determine whether or not the function g(x)=∣2x−4∣g ( x ) = | 2 x - 4 |g(x)=∣2x−4∣ is one-to-one.

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 intervals on which the function is increasing and on which the function is decreasing.

Fundamentals

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions: Unit Circle Approach

Trigonometric Functions: Right Triangle Approach

Analytic Trigonometry

Polar Coordinates and Parametric Equations

Vectors in Two and Three Dimensions

Systems of Equations and Inequalities

Conic Sections

Sequences and Series

Limits: a Preview of Calculus

Filters

The graph of $f ( x ) = | x | - 3$ is shown. Use this graph to sketch the graph of $g ( x ) = | | x | - 3 |$ .

For the function $f ( x ) = \frac { 2 } { 3 } x ^ { 4 } - \frac { 1 } { 3 } x ^ { 5 } - x + 3$ determine the average rate of change between the values $x = - 1$ and $x = 1 .$

Determine whether or not the function $h ( x ) = 3 x ^ { 6 } + 2$ , $0 \leq x \leq \infty$ is one-to-one.

Use a graphing device to the graph of the function $f ( x ) = x ^ { 4 } + 2 x ^ { 3 } - 3 x ^ { 2 } - 4 x + 4$ . State approximately the intervals on which the function is increasing and on which the function is decreasing.

Find the domain of the function $h ( x ) = \sqrt { 2 x ^ { 2 } + 3 x + 1 }$ .

The graph of a function is given. Determine the average rate of change of the function between the indicated points on the graph. (2,8) $( - 2 , - 8 )$

Express the function $H ( x ) = \left( 2 + x ^ { 2 } \right) ^ { 3 }$ in the form $f \circ g$ .

Let $f ( x ) = x ^ { 3 } + c$ . Graph the family of functions with $c = - 4$ , $- 2$ , $0$ , $2$ , and $4$ in the viewing rectangle $[ - 5,5 ]$ by $[ - 5,5 ]$ . How does the value of $c$ affect the graph?

Use $f ( x ) = x - 4$ and $g ( x ) = 2 - x ^ { 2 }$ to evaluate the expression $g ( g ( 1 ) )$ .

Determine if the equation $x ^ { 2 } + y ^ { 2 } - 25 = 0$ defines $y$ as a function of $x$ . Explain your answer.

Determine whether or not the function $g ( x ) = | 2 x - 4 |$ is one-to-one.

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