Question 1

Complete the table for the function $f ( x ) = \left| 3 - 2 x ^ { 2 } \right|$ .
$$\begin{array} { | c | c | } 
\hline x & \begin{array} { c } 
f ( x ) \
\end{array} \
\hline - 2 & \
\hline 0 & \
\hline 1 & \
\hline 3 & \
\hline 5 & \
\hline
\end{array}$$

Accepted Answer

None

Question 2

The graph shows the depth of water W in a reservoir over a one-year period as a function of the number of days x since the beginning of the year. What was the average rate of change of W between x = 100 and x= 200?

Accepted Answer

The answer of The graph shows the depth of water...

Question 3

The graph shows the depth of water W in a reservoir over a one-year period as a function of the number of days x since the beginning of the year. Estimate the average rate of change of W between x = 200 and x= 300.

Accepted Answer

The answer of The graph shows the depth of water...

Question 4

If $\$ 10,000$ is invested for $x$ years at $5 \%$ simple interest, the total amount $A$ of the investment is given by the function $$A ( x ) = 500 x + 10,000$$ .(a) Find $A ^ { - 1 }$ . 
(b) Find
 $A ^ { - 1 } ( 16,500 )$ . What does your answer represent?

Accepted Answer

(a) Let @#LAT-DLM& @#LAT-DLM& @#LAT-DLM& @#LAT-DLM& @#LAT-DLM& @#LAT-DLM& @#LAT-DLM& .
(b) @#LAT-DLM& years, t

Question 5

If $f ( x ) = 3 x ^ { 2 } + x - 2$ , find $f ( 0 )$ , $f ( 1 )$ , $f ( - 1 )$ .

Accepted Answer

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

Question 6

For the function $f ( x ) = \sqrt { 4 x }$ determine the average rate of change between the values $x = a$ and $x = a + h$ .

Accepted Answer

Average ra

Question 7

Determine if the equation $2 x ^ { 2 } + 3 y = 4 x + 5$ defines $y$ as a function of $x$ . Explain your answer.

Accepted Answer

@#LAT-DLM& @#LAT-DLM& @#LAT-DLM& @#LAT-DLM& @#LAT-DLM& . The last equa

Question 8

Use a graphing calculator or computer to draw a graph of $f ( x ) = 3 x ^ { 3 } - 2$ and determine whether the function is one-to-one.

Accepted Answer

From the g

Question 9

A function is given. Use a graphing calculator to draw the graph of f. Find the domain and range of f from the graph. $f ( x ) = \sqrt { 9 - x ^ { 2 } }$

Accepted Answer

The answer of A function is given. Use a graphing...

Question 10

Use $f ( x ) = x - 2$ and $g ( x ) = 4 - 2 x ^ { 2 }$ to evaluate the expression $g ( f ( 0 ) )$ .

Accepted Answer

A)  $- 3$ 
B)  $- 2$ 
C)  $- 4$ 
D)  $0$ 
E)  $1$ 
A)  $- 3$ 
B)  $- 2$ 
C)  $- 4$ 
D)  $0$ 
E)  $1$

Question 11

Find the inverse function of $f ( x ) = x ^ { 2 } - 4 x + 9$ , $x \geq 2$ .

Accepted Answer

@#LAT-DLM&
Compete the square

Question 12

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

Accepted Answer

A)  $- 1$ 
B)  $- x ^ { 2 }$ 
C)  $x ^ { 2 }$ 
D)  $x$ 
E)  $0$ 
A)  $- 1$ 
B)  $- x ^ { 2 }$ 
C)  $x ^ { 2 }$ 
D)  $x$ 
E)  $0$

Question 13

Express the rule in function notation. Multiply by $4$ , then subtract $2$ .

Accepted Answer

A)  $f ( x ) = 2 x + 4$ 
B)  $f ( x ) = - 18 x$ 
C)  $f ( x ) = 4 x - 2$ 
D)  $f ( x ) = 4 ( x + 2 )$ 
E)  $f ( x ) = 4 ( x - 2 )$ 
A)  $f ( x ) = 2 x + 4$ 
B)  $f ( x ) = - 18 x$ 
C)  $f ( x ) = 4 x - 2$ 
D)  $f ( x ) = 4 ( x + 2 )$ 
E)  $f ( x ) = 4 ( x - 2 )$

Question 14

Let $f ( x ) = 2 x - 1$ and $g ( x ) = x ^ { 2 } + 3 x - 5$ . Find $f + g$ , $f / g$ and their domains.

Accepted Answer

@#LAT-DLM& , domain is @#LAT-DLM& ; @#LAT-DLM& , d

Question 15

Use the Property of Inverse Functions to show that $f ( x ) = \frac { 3 x - 5 } { 5 }$ and $g ( x ) = \frac { 5 } { 3 } x + \frac { 5 } { 3 }$ are inverses of each other.

Accepted Answer

The answer of Use the Property of Inverse Functions to...

Question 16

Use $f ( x ) = 3 x - 2$ and $g ( x ) = 3 + 2 x ^ { 2 }$ to evaluate the expression $( f \circ g ) ( 2 )$ .

Accepted Answer

A)  $31$ 
B)  $14$ 
C)  $39$ 
D)  $11$ 
E)  $114$ 
A)  $31$ 
B)  $14$ 
C)  $39$ 
D)  $11$ 
E)  $114$

Question 17

For the linear function $f ( x ) = 5 - 5 x$ , find the average rate of change between $x = a$ and $x = a + h$ . Show that the average rate of change is the same as the slope of the line.

Accepted Answer

The slope of the lin

Question 18

If $n ( t ) = \frac { | t - 1 | } { t - 1 }$ , find $h ( - 2 )$ , $h ( - 1 )$ , $h ( 0 )$ , $h ( 2 )$ , and $h ( a + 1 )$ .

Accepted Answer

None

Complete the table for the function $f ( x ) = \left| 3 - 2 x ^ { 2 } \right|$ . x f(x) -2 0 1 3 5

The graph shows the depth of water W in a reservoir over a one-year period as a function of the number of days x since the beginning of the year. What was the average rate of change of W between x = 100 and x= 200?

The graph shows the depth of water W in a reservoir over a one-year period as a function of the number of days x since the beginning of the year. Estimate the average rate of change of W between x = 200 and x= 300.

If $\$ 10,000$ is invested for $x$ years at $5 \%$ simple interest, the total amount $A$ of the investment is given by the function $A ( x ) = 500 x + 10,000$ .(a) Find $A ^ { - 1 }$ . (b) Find $A ^ { - 1 } ( 16,500 )$ . What does your answer represent?

If $f ( x ) = 3 x ^ { 2 } + x - 2$ , find $f ( 0 )$ , $f ( 1 )$ , $f ( - 1 )$ .

For the function $f ( x ) = \sqrt { 4 x }$ determine the average rate of change between the values $x = a$ and $x = a + h$ .

Determine if the equation $2 x ^ { 2 } + 3 y = 4 x + 5$ defines $y$ as a function of $x$ . Explain your answer.

Use a graphing calculator or computer to draw a graph of $f ( x ) = 3 x ^ { 3 } - 2$ and determine whether the function is one-to-one.

A function is given. Use a graphing calculator to draw the graph of f. Find the domain and range of f from the graph. $f ( x ) = \sqrt { 9 - x ^ { 2 } }$

Use $f ( x ) = x - 2$ and $g ( x ) = 4 - 2 x ^ { 2 }$ to evaluate the expression $g ( f ( 0 ) )$ .

Find the inverse function of $f ( x ) = x ^ { 2 } - 4 x + 9$ , $x \geq 2$ .

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

Express the rule in function notation. Multiply by $4$ , then subtract $2$ .

Let $f ( x ) = 2 x - 1$ and $g ( x ) = x ^ { 2 } + 3 x - 5$ . Find $f + g$ , $f / g$ and their domains.

Use the Property of Inverse Functions to show that $f ( x ) = \frac { 3 x - 5 } { 5 }$ and $g ( x ) = \frac { 5 } { 3 } x + \frac { 5 } { 3 }$ are inverses of each other.

Use $f ( x ) = 3 x - 2$ and $g ( x ) = 3 + 2 x ^ { 2 }$ to evaluate the expression $( f \circ g ) ( 2 )$ .

For the linear function $f ( x ) = 5 - 5 x$ , find the average rate of change between $x = a$ and $x = a + h$ . Show that the average rate of change is the same as the slope of the line.

If $n ( t ) = \frac { | t - 1 | } { t - 1 }$ , find $h ( - 2 )$ , $h ( - 1 )$ , $h ( 0 )$ , $h ( 2 )$ , and $h ( a + 1 )$ .

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

Complete the table for the function f(x)=∣3−2x2∣f ( x ) = \left| 3 - 2 x ^ { 2 } \right|f(x)=​3−2x2​ . x f(x) -2 0 1 3 5

The graph shows the depth of water W in a reservoir over a one-year period as a function of the number of days x since the beginning of the year. What was the average rate of change of W between x = 100 and x= 200?

The graph shows the depth of water W in a reservoir over a one-year period as a function of the number of days x since the beginning of the year. Estimate the average rate of change of W between x = 200 and x= 300.

If f(x)=3x2+x−2f ( x ) = 3 x ^ { 2 } + x - 2f(x)=3x2+x−2 , find f(0)f ( 0 )f(0) , f(1)f ( 1 )f(1) , f(−1)f ( - 1 )f(−1) .

For the function f(x)=4xf ( x ) = \sqrt { 4 x }f(x)=4x​ determine the average rate of change between the values x=ax = ax=a and x=a+hx = a + hx=a+h .

Determine if the equation 2x2+3y=4x+52 x ^ { 2 } + 3 y = 4 x + 52x2+3y=4x+5 defines yyy as a function of xxx . Explain your answer.

Use a graphing calculator or computer to draw a graph of f(x)=3x3−2f ( x ) = 3 x ^ { 3 } - 2f(x)=3x3−2 and determine whether the function is one-to-one.

A function is given. Use a graphing calculator to draw the graph of f. Find the domain and range of f from the graph. f(x)=9−x2f ( x ) = \sqrt { 9 - x ^ { 2 } }f(x)=9−x2​

Use f(x)=x−2f ( x ) = x - 2f(x)=x−2 and g(x)=4−2x2g ( x ) = 4 - 2 x ^ { 2 }g(x)=4−2x2 to evaluate the expression g(f(0))g ( f ( 0 ) )g(f(0)) .

Find the inverse function of f(x)=x2−4x+9f ( x ) = x ^ { 2 } - 4 x + 9f(x)=x2−4x+9 , x≥2x \geq 2x≥2 .

Use f(x)=x2−1f ( x ) = x ^ { 2 } - 1f(x)=x2−1 and g(x)=−x+1g ( x ) = - \sqrt { x + 1 }g(x)=−x+1​ to evaluate the expression (f∘g)(x)( f \circ g ) ( x )(f∘g)(x) .

Express the rule in function notation. Multiply by 444 , then subtract 222 .

Let f(x)=2x−1f ( x ) = 2 x - 1f(x)=2x−1 and g(x)=x2+3x−5g ( x ) = x ^ { 2 } + 3 x - 5g(x)=x2+3x−5 . Find f+gf + gf+g , f/gf / gf/g and their domains.

Use the Property of Inverse Functions to show that f(x)=3x−55f ( x ) = \frac { 3 x - 5 } { 5 }f(x)=53x−5​ and g(x)=53x+53g ( x ) = \frac { 5 } { 3 } x + \frac { 5 } { 3 }g(x)=35​x+35​ are inverses of each other.

Use 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 to evaluate the expression (f∘g)(2)( f \circ g ) ( 2 )(f∘g)(2) .

For the linear function f(x)=5−5xf ( x ) = 5 - 5 xf(x)=5−5x , find the average rate of change between x=ax = ax=a and x=a+hx = a + hx=a+h . Show that the average rate of change is the same as the slope of the line.

If n(t)=∣t−1∣t−1n ( t ) = \frac { | t - 1 | } { t - 1 }n(t)=t−1∣t−1∣​ , find h(−2)h ( - 2 )h(−2) , h(−1)h ( - 1 )h(−1) , h(0)h ( 0 )h(0) , h(2)h ( 2 )h(2) , and h(a+1)h ( a + 1 )h(a+1) .

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

Complete the table for the function $f ( x ) = \left| 3 - 2 x ^ { 2 } \right|$ . x f(x) -2 0 1 3 5

If $f ( x ) = 3 x ^ { 2 } + x - 2$ , find $f ( 0 )$ , $f ( 1 )$ , $f ( - 1 )$ .

For the function $f ( x ) = \sqrt { 4 x }$ determine the average rate of change between the values $x = a$ and $x = a + h$ .

Determine if the equation $2 x ^ { 2 } + 3 y = 4 x + 5$ defines $y$ as a function of $x$ . Explain your answer.

Use a graphing calculator or computer to draw a graph of $f ( x ) = 3 x ^ { 3 } - 2$ and determine whether the function is one-to-one.

A function is given. Use a graphing calculator to draw the graph of f. Find the domain and range of f from the graph. $f ( x ) = \sqrt { 9 - x ^ { 2 } }$

Use $f ( x ) = x - 2$ and $g ( x ) = 4 - 2 x ^ { 2 }$ to evaluate the expression $g ( f ( 0 ) )$ .

Find the inverse function of $f ( x ) = x ^ { 2 } - 4 x + 9$ , $x \geq 2$ .

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

Express the rule in function notation. Multiply by $4$ , then subtract $2$ .

Let $f ( x ) = 2 x - 1$ and $g ( x ) = x ^ { 2 } + 3 x - 5$ . Find $f + g$ , $f / g$ and their domains.

Use the Property of Inverse Functions to show that $f ( x ) = \frac { 3 x - 5 } { 5 }$ and $g ( x ) = \frac { 5 } { 3 } x + \frac { 5 } { 3 }$ are inverses of each other.

Use $f ( x ) = 3 x - 2$ and $g ( x ) = 3 + 2 x ^ { 2 }$ to evaluate the expression $( f \circ g ) ( 2 )$ .

For the linear function $f ( x ) = 5 - 5 x$ , find the average rate of change between $x = a$ and $x = a + h$ . Show that the average rate of change is the same as the slope of the line.

If $n ( t ) = \frac { | t - 1 | } { t - 1 }$ , find $h ( - 2 )$ , $h ( - 1 )$ , $h ( 0 )$ , $h ( 2 )$ , and $h ( a + 1 )$ .