Question 1

Graph the function:

Accepted Answer

The answer of Graph the function:
 ...

Question 2

The graph of $g(x)=\sqrt{25-x^{2}}$ is shown below. What is the range of $g(x)$ ?

Accepted Answer

A)  $0 \leq y \leq 5$ 
B)  $y \leq 5$ 
C)  $y \geq 0$ 
D)  $-5 \leq y \leq 5$ 
A)  $0 \leq y \leq 5$ 
B)  $y \leq 5$ 
C)  $y \geq 0$ 
D)  $-5 \leq y \leq 5$

Question 3

The car slowed down steadily. Which of the following graphs shows the velocity graphed against time?

Accepted Answer

A)    
B)    
C)    
D)    
E)    
F)   
A)    
B)    
C)    
D)    
E)    
F)

Question 4

The circumference, in $\mathrm{cm}$, of a circle whose radius is $r \mathrm{~cm}$ is given by $C=2 \pi r$. If $C=f(r)$, evaluate and interpret $f(r)+5$.

Accepted Answer

A)  $2 \pi r+5$, the circumference of a circle of radius $r+5$. 
B)  $2 \pi r+5,5$ more than the circumference of a circle of radius $r$. 
C)  $2 \pi r+10 \pi$, the circumference of a circle of radius $r+5$. 
D)  $2 \pi r+10 \pi, 5$ more than the circumference of a circle of radius $r$. 
A)  $2 \pi r+5$, the circumference of a circle of radius $r+5$. 
B)  $2 \pi r+5,5$ more than the circumference of a circle of radius $r$. 
C)  $2 \pi r+10 \pi$, the circumference of a circle of radius $r+5$. 
D)  $2 \pi r+10 \pi, 5$ more than the circumference of a circle of radius $r$.

Question 5

Which of the following is a piecewise formula for the function $f(x)=|3 x-15|$

Accepted Answer

A)  $f(x)= \begin{cases}15-3 x, & x \leq 5 \ 3 x-15, & x>5\end{cases}$ 
B)  $f(x)= \begin{cases}3 x-15, & x \leq 5 \ 15-3 x, & x>5\end{cases}$ 
C)  $f(x)= \begin{cases}15-3 x, & x \leq 15 \ 3 x-15, & x>15\end{cases}$ 
D)  $f(x)= \begin{cases}3 x-15, & x \leq 15 \ 15-3 x, & x>15\end{cases}$ 
A)  $f(x)= \begin{cases}15-3 x, & x \leq 5 \ 3 x-15, & x>5\end{cases}$ 
B)  $f(x)= \begin{cases}3 x-15, & x \leq 5 \ 15-3 x, & x>5\end{cases}$ 
C)  $f(x)= \begin{cases}15-3 x, & x \leq 15 \ 3 x-15, & x>15\end{cases}$ 
D)  $f(x)= \begin{cases}3 x-15, & x \leq 15 \ 15-3 x, & x>15\end{cases}$

Question 6

Let  
  
a) Evaluate $f(0)$.
b) Evaluate $f(-1)$.
c) Evaluate $f(3)$.

Accepted Answer

The answer of Let  
  
a) Evaluate $f(0)$.
b)...

Question 7

The graph of $f(x)$ contains the point $(3,1)$. What is the corresponding point on the graph of $f(x+5)$ ?

Accepted Answer

The answer of The graph of $f(x)$ contains the point...

Question 8

If $f(x)=\frac{1}{x+6}+5$, find $f(-1)$ to 2 decimal places.

Accepted Answer

The answer of If $f(x)=\frac{1}{x+6}+5$, find $f(-1)$ to 2 decimal...

Question 9

What is the domain of the function $f(x)=\frac{10}{\sqrt{1-x^{2}}}$ ?

Accepted Answer

A)   
B)    
C)    
D)   
A)   
B)    
C)    
D)

Question 10

Let $f(x)=\ln x$ and $g(x)=\ln (x+5)$ for $x>0$. How does the graph of $g(x)$ compare to the graph of $f(x)$ ?

Accepted Answer

A)  The graph of $g(x)$ is 5 units up. 
B)  The graph of $g(x)$ is 5 units down. 
C)  The graph of $g(x)$ is 5 units to the right. 
D)  The graph of $g(x)$ is 5 units to the left. 
A)  The graph of $g(x)$ is 5 units up. 
B)  The graph of $g(x)$ is 5 units down. 
C)  The graph of $g(x)$ is 5 units to the right. 
D)  The graph of $g(x)$ is 5 units to the left.

Question 11

Let $f(x)= \begin{cases}2 x-5, & x \leq 0 \ 3 x+8, & x>0\end{cases}$
a) Find the domain of $f$
b) Find the range of $f$

Accepted Answer

a) domain: all real

Question 12

Given the function $f(x)=\sqrt{x-3}$, find the range of $f^{-1}(x)$.

Accepted Answer

The answer of Given the function $f(x)=\sqrt{x-3}$, find the range...

Question 13

Let $f(x)=\frac{3 x+9}{2 x+1}$. For what value of $x$ is $f(x)=3$ ?

Accepted Answer

The answer of Let $f(x)=\frac{3 x+9}{2 x+1}$. For what value...

Question 14

Let

a) What is the domain of $f$ ?
b) What is the range of $f$ ?

Accepted Answer

a) Domain: @#LAT-DLM&
b) Range

Question 15

Find the inverse for the function $y=f(x)=x^{4}+5$.

Accepted Answer

The answer of Find the inverse for the function $y=f(x)=x^{4}+5$....

Question 16

A supermarket only sells cans of soda in 6-packs. The price of a 6-pack is $\$ 1.85$. Let $C(x)$ be the total cost if you need $x$ cans of soda. What is the range of $C(x)$ ?

Accepted Answer

A)  All nonnegative multiples of 6 . 
B)  All nonnegative multiples of 1.85 . 
C)  All nonnegative multiples of $1.85 * 6$. 
D)  All real numbers. 
A)  All nonnegative multiples of 6 . 
B)  All nonnegative multiples of 1.85 . 
C)  All nonnegative multiples of $1.85 * 6$. 
D)  All real numbers.

Question 17

Find the domain and range of the function $h(x)=\frac{-3}{x^{2}+4}$

Accepted Answer

Domain : A

Question 18

Suppose that your uncle Gerald has just opened a store that sells television sets. Let $P(x)$ represent the profit that he makes selling $x$ television sets per week. Suppose that he currently sells $k$ television sets per week. What is the practical interpretation of $P(2 k)$ ?

Accepted Answer

A)  Twice the profit he currently makes. 
B)  The number of additional television sets he would have to sell per week to obtain twice the profit. 
C)  The profit he would make if he sold twice as many television sets per week than he currently sells. 
D)  Twice the number of television sets he currently sells. 
A)  Twice the profit he currently makes. 
B)  The number of additional television sets he would have to sell per week to obtain twice the profit. 
C)  The profit he would make if he sold twice as many television sets per week than he currently sells. 
D)  Twice the number of television sets he currently sells.

Question 19

Determine the concavity of the graph of $f(x)=-x^{2}-x-8$ between $x=-1$ and $x=2$ by calculating average rates of change over intervals of length 1 . Is the graph concave up or concave down?

Accepted Answer

The answer of Determine the concavity of the graph of...

Question 20

If $f(x)=4 x^{2}+5 x$ and $g(x)=f(x-3)$, what is $g(3)$ ?

Accepted Answer

The answer of If $f(x)=4 x^{2}+5 x$ and $g(x)=f(x-3)$, what...

Graph the function:

The graph of $g(x)=\sqrt{25-x^{2}}$ is shown below. What is the range of $g(x)$ ? $The graph of g(x)=\sqrt{25-x^{2}} is shown below. What is the range of g(x) ?$

The car slowed down steadily. Which of the following graphs shows the velocity graphed against time?

The circumference, in $\mathrm{cm}$ , of a circle whose radius is $r \mathrm{~cm}$ is given by $C=2 \pi r$ . If $C=f(r)$ , evaluate and interpret $f(r)+5$ .

Which of the following is a piecewise formula for the function $f(x)=|3 x-15|$

Let a) Evaluate $f(0)$ . b) Evaluate $f(-1)$ . c) Evaluate $f(3)$ .

The graph of $f(x)$ contains the point $(3,1)$ . What is the corresponding point on the graph of $f(x+5)$ ?

If $f(x)=\frac{1}{x+6}+5$ , find $f(-1)$ to 2 decimal places.

What is the domain of the function $f(x)=\frac{10}{\sqrt{1-x^{2}}}$ ?

Let $f(x)=\ln x$ and $g(x)=\ln (x+5)$ for $x>0$ . How does the graph of $g(x)$ compare to the graph of $f(x)$ ?

Let $f(x)= \begin{cases}2 x-5, & x \leq 0 \\ 3 x+8, & x>0\end{cases}$ a) Find the domain of $f$ b) Find the range of $f$

Given the function $f(x)=\sqrt{x-3}$ , find the range of $f^{-1}(x)$ .

Let $f(x)=\frac{3 x+9}{2 x+1}$ . For what value of $x$ is $f(x)=3$ ?

Let a) What is the domain of $f$ ? b) What is the range of $f$ ?

Find the inverse for the function $y=f(x)=x^{4}+5$ .

A supermarket only sells cans of soda in 6-packs. The price of a 6-pack is $\$ 1.85$ . Let $C(x)$ be the total cost if you need $x$ cans of soda. What is the range of $C(x)$ ?

Find the domain and range of the function $h(x)=\frac{-3}{x^{2}+4}$

Suppose that your uncle Gerald has just opened a store that sells television sets. Let $P(x)$ represent the profit that he makes selling $x$ television sets per week. Suppose that he currently sells $k$ television sets per week. What is the practical interpretation of $P(2 k)$ ?

Determine the concavity of the graph of $f(x)=-x^{2}-x-8$ between $x=-1$ and $x=2$ by calculating average rates of change over intervals of length 1 . Is the graph concave up or concave down?

If $f(x)=4 x^{2}+5 x$ and $g(x)=f(x-3)$ , what is $g(3)$ ?

Linear Functions and Change

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Exponential Functions

Logarithmic Functions

Transformations of Functions and Their Graphs

Trigonometry and Periodic Functions

Triangle Trigonometry and Polar Coordinates

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Exam 2: Functions

Graph the function:

The graph of g(x)=25−x2g(x)=\sqrt{25-x^{2}}g(x)=25−x2​ is shown below. What is the range of g(x)g(x)g(x) ?

The car slowed down steadily. Which of the following graphs shows the velocity graphed against time?

The circumference, in cm\mathrm{cm}cm , of a circle whose radius is r cmr \mathrm{~cm}r cm is given by C=2πrC=2 \pi rC=2πr . If C=f(r)C=f(r)C=f(r) , evaluate and interpret f(r)+5f(r)+5f(r)+5 .

Which of the following is a piecewise formula for the function f(x)=∣3x−15∣f(x)=|3 x-15|f(x)=∣3x−15∣

Let a) Evaluate f(0)f(0)f(0) . b) Evaluate f(−1)f(-1)f(−1) . c) Evaluate f(3)f(3)f(3) .

The graph of f(x)f(x)f(x) contains the point (3,1)(3,1)(3,1) . What is the corresponding point on the graph of f(x+5)f(x+5)f(x+5) ?

If f(x)=1x+6+5f(x)=\frac{1}{x+6}+5f(x)=x+61​+5 , find f(−1)f(-1)f(−1) to 2 decimal places.

What is the domain of the function f(x)=101−x2f(x)=\frac{10}{\sqrt{1-x^{2}}}f(x)=1−x2​10​ ?

Let f(x)=ln⁡xf(x)=\ln xf(x)=lnx and g(x)=ln⁡(x+5)g(x)=\ln (x+5)g(x)=ln(x+5) for x>0x>0x>0 . How does the graph of g(x)g(x)g(x) compare to the graph of f(x)f(x)f(x) ?

Let f(x)={2x−5,x≤03x+8,x>0f(x)= \begin{cases}2 x-5, & x \leq 0 \\ 3 x+8, & x>0\end{cases}f(x)={2x−5,3x+8,​x≤0x>0​ a) Find the domain of fff b) Find the range of fff

Given the function f(x)=x−3f(x)=\sqrt{x-3}f(x)=x−3​ , find the range of f−1(x)f^{-1}(x)f−1(x) .

Let f(x)=3x+92x+1f(x)=\frac{3 x+9}{2 x+1}f(x)=2x+13x+9​ . For what value of xxx is f(x)=3f(x)=3f(x)=3 ?

Let a) What is the domain of fff ? b) What is the range of fff ?

Find the inverse for the function y=f(x)=x4+5y=f(x)=x^{4}+5y=f(x)=x4+5 .

A supermarket only sells cans of soda in 6-packs. The price of a 6-pack is $1.85\$ 1.85$1.85 . Let C(x)C(x)C(x) be the total cost if you need xxx cans of soda. What is the range of C(x)C(x)C(x) ?

Find the domain and range of the function h(x)=−3x2+4h(x)=\frac{-3}{x^{2}+4}h(x)=x2+4−3​

Suppose that your uncle Gerald has just opened a store that sells television sets. Let P(x)P(x)P(x) represent the profit that he makes selling xxx television sets per week. Suppose that he currently sells kkk television sets per week. What is the practical interpretation of P(2k)P(2 k)P(2k) ?

Determine the concavity of the graph of f(x)=−x2−x−8f(x)=-x^{2}-x-8f(x)=−x2−x−8 between x=−1x=-1x=−1 and x=2x=2x=2 by calculating average rates of change over intervals of length 1 . Is the graph concave up or concave down?

If f(x)=4x2+5xf(x)=4 x^{2}+5 xf(x)=4x2+5x and g(x)=f(x−3)g(x)=f(x-3)g(x)=f(x−3) , what is g(3)g(3)g(3) ?

Linear Functions and Change

Quadratic Functions

Exponential Functions

Logarithmic Functions

Transformations of Functions and Their Graphs

Trigonometry and Periodic Functions

Triangle Trigonometry and Polar Coordinates

Trigonometric Identities, Models, and Complex Numbers

Compositions, Inverses, and Combinations of Functions

Polynomial and Rational Functions

Vectors and Matrices

Sequences and Series

Parametric Equations and Conic Sections

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The graph of $g(x)=\sqrt{25-x^{2}}$ is shown below. What is the range of $g(x)$ ? $The graph of g(x)=\sqrt{25-x^{2}} is shown below. What is the range of g(x) ?$

The circumference, in $\mathrm{cm}$ , of a circle whose radius is $r \mathrm{~cm}$ is given by $C=2 \pi r$ . If $C=f(r)$ , evaluate and interpret $f(r)+5$ .

Which of the following is a piecewise formula for the function $f(x)=|3 x-15|$

Let a) Evaluate $f(0)$ . b) Evaluate $f(-1)$ . c) Evaluate $f(3)$ .

The graph of $f(x)$ contains the point $(3,1)$ . What is the corresponding point on the graph of $f(x+5)$ ?

If $f(x)=\frac{1}{x+6}+5$ , find $f(-1)$ to 2 decimal places.

What is the domain of the function $f(x)=\frac{10}{\sqrt{1-x^{2}}}$ ?

Let $f(x)=\ln x$ and $g(x)=\ln (x+5)$ for $x>0$ . How does the graph of $g(x)$ compare to the graph of $f(x)$ ?

Let $f(x)= \begin{cases}2 x-5, & x \leq 0 \\ 3 x+8, & x>0\end{cases}$ a) Find the domain of $f$ b) Find the range of $f$

Given the function $f(x)=\sqrt{x-3}$ , find the range of $f^{-1}(x)$ .

Let $f(x)=\frac{3 x+9}{2 x+1}$ . For what value of $x$ is $f(x)=3$ ?

Let a) What is the domain of $f$ ? b) What is the range of $f$ ?

Find the inverse for the function $y=f(x)=x^{4}+5$ .

A supermarket only sells cans of soda in 6-packs. The price of a 6-pack is $\$ 1.85$ . Let $C(x)$ be the total cost if you need $x$ cans of soda. What is the range of $C(x)$ ?

Find the domain and range of the function $h(x)=\frac{-3}{x^{2}+4}$

Suppose that your uncle Gerald has just opened a store that sells television sets. Let $P(x)$ represent the profit that he makes selling $x$ television sets per week. Suppose that he currently sells $k$ television sets per week. What is the practical interpretation of $P(2 k)$ ?

Determine the concavity of the graph of $f(x)=-x^{2}-x-8$ between $x=-1$ and $x=2$ by calculating average rates of change over intervals of length 1 . Is the graph concave up or concave down?

If $f(x)=4 x^{2}+5 x$ and $g(x)=f(x-3)$ , what is $g(3)$ ?