Question 1

Which of the following could be a formula for the graph shown below?

Accepted Answer

A)  $y=(x-20)^{2}+100$ 
B)  $y=250(0.9552)^{x}$ 
C)  $y=\frac{x+250}{x+1}$ 
D)  $y=-\frac{15}{2} x+250$ 
E)  $y=\frac{250}{(20)^{x}}$ 
A)  $y=(x-20)^{2}+100$ 
B)  $y=250(0.9552)^{x}$ 
C)  $y=\frac{x+250}{x+1}$ 
D)  $y=-\frac{15}{2} x+250$ 
E)  $y=\frac{250}{(20)^{x}}$ B

Question 2

Which of the following could be a formula for the graph shown below?

Accepted Answer

A)  $-\frac{1}{9}(x+3)^{2}(x-2)$ 
B)  $(x+3)^{2}(x-2)$ 
C)  $-\frac{1}{3}(x+3)(x-2)$ 
D)  $-(x+3)(x-2)$ 
A)  $-\frac{1}{9}(x+3)^{2}(x-2)$ 
B)  $(x+3)^{2}(x-2)$ 
C)  $-\frac{1}{3}(x+3)(x-2)$ 
D)  $-(x+3)(x-2)$ A

Question 3

Simplify   , if possible.

Accepted Answer

$\frac{30}{\left(x^{3}+y\right)\left(x+y^{4}\right)}$

Question 4

The squirrel population in a certain area is estimated each year and recorded in the table below. Suppose the squirrel population in a given year is a function of the number of years since 1998. Fit an exponential function to the data and use it to estimate the squirrel population (rounded to the nearest whole number) in 2013.

Accepted Answer

The answer of The squirrel population in a certain area...

Question 5

What are the zeros of $f(x)=x^{7}+4 x^{2}-3$ ? List them in ascending order separated by commas, and round any non-integer zeros to 3 decimal places.

Accepted Answer

The answer of What are the zeros of $f(x)=x^{7}+4 x^{2}-3$...

Question 6

Write a formula for a function, $f(x)$, whose graph is identical to the graph of $y=x^{4}$, except that the graph has holes at $(-3,81)$ and $(5,625)$. Express the function $f(x)$ has a rational function.

Accepted Answer

The answer of Write a formula for a function, $f(x)$,...

Question 7

The squirrel population in a certain area is estimated each year and recorded in the table below. Suppose the squirrel population in a given year is a function of the number of years since 1998. Fit a cubic function to the data and use it to estimate the squirrel population (rounded to the nearest whole number) in 2011.

Accepted Answer

The answer of The squirrel population in a certain area...

Question 8

Which of the following graphs show $p$ being proportional to the square of $q$ ?

Accepted Answer

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

Question 9

Which of the following are rational functions:

Accepted Answer

A)  $y=\frac{x^{2}-3}{x^{4}}-\frac{1}{4 x^{2}}$ 
B)  $y=\frac{3^{x}-4}{3^{x}}$ 
C)  $y=\frac{3 \sqrt{x}+4}{x^{3}-4}$ 
D)  $y=\frac{3 x^{-4}}{3+x^{4}}+\frac{x^{-3}}{1-x^{-3}}$ 
A)  $y=\frac{x^{2}-3}{x^{4}}-\frac{1}{4 x^{2}}$ 
B)  $y=\frac{3^{x}-4}{3^{x}}$ 
C)  $y=\frac{3 \sqrt{x}+4}{x^{3}-4}$ 
D)  $y=\frac{3 x^{-4}}{3+x^{4}}+\frac{x^{-3}}{1-x^{-3}}$

Question 10

If $f(x)=x^{2}-3$ and $g(x)=\frac{x^{4}}{2}-7$, then $f(x)>g(x)$ on the interval ----------- (<x<)-------------.

Accepted Answer

Part A: -2

Question 11

What are the $x$-intercepts, $y$-intercepts, and horizontal asymptotes of the function $y=\frac{16 x^{2}-8 x-8}{x^{4}+8 x+32}$

Accepted Answer

None

Question 12

It is possible for a rational function to have horizontal asymptotes at $y=2$ and $y=-6$.

Accepted Answer

A) True 
 B)False

Question 13

The formula for the function graphed below has leading term $a x^{n}$ (i.e. $f(x)=a x^{n}+$ terms of lower degree). If $n$ is as small as possible, then $n=$ ---------- and a= ----------

Accepted Answer

Part A: 4

Question 14

Which of the following could be a formula for the graph shown below?

Accepted Answer

A)  $y=\frac{(x-1)(x-1.5)}{(x+4)(x+6)}$ 
B)  $y=\frac{4 x+1.5}{x+4}$ 
C)  $y=\frac{x+6}{x+4}$ 
D)  $y=\frac{x-6}{x+4}$ 
A)  $y=\frac{(x-1)(x-1.5)}{(x+4)(x+6)}$ 
B)  $y=\frac{4 x+1.5}{x+4}$ 
C)  $y=\frac{x+6}{x+4}$ 
D)  $y=\frac{x-6}{x+4}$

Question 15

The following figure gives the graphs of four power functions. Which one could be the graph of $y=1000 x^{-4}$ ? If none of the graphs match, enter "none".

Accepted Answer

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

Question 16

The formula for the power function whose values are in the following table is $y=k x^{p}$, where $k=$ --------- and $p=$-----------

Accepted Answer

The answer of The formula for the power function whose...

Question 17

Determine the vertical and horizontal asymptotes, if they exist, of the function
$y=3-\frac{13}{2 x+12}+\frac{1}{5 x^{4}}$

Accepted Answer

Vertical a

Question 18

George measures the force exerted by a certain spring when it is stretched various distances beyond its natural length. The data he gathers is compiled in the following table. He wishes to describe the force as a function of the stretched distance, and decides to use a quadratic function model. After fitting a quadratic function to the data, he uses it to estimate the force when the spring is stretched 17 inches. What is his approximation (to three decimal places) of this force?
$\begin{array}{llllll}\text { Stretched Distance (feet) } & 0.17 & 0.56 & 0.73 & 0.81 & 1.13\end{array}$
$\begin{array}{llllll}\text { Force (pounds) } & 16.74 & 499.82 & 1,180.23 & 1,645.11 & 4,102.94\end{array}$

Accepted Answer

The answer of George measures the force exerted by a...

Question 19

The polynomial $f$ graphed below has leading term $a x^{n}$ (i.e. $f(x)=a x^{n}+$ terms of lower degree). We know that $a$ is ----------- (positive \ negative), $n$ is ------------- (even \ odd), and the smallest possible value of $n$ is ----------------------.

Accepted Answer

Part A: po

Question 20

It is possible for a rational function $f$ to have no zeros, such that $f(x)0$ for $x>7$

Accepted Answer

A) True 
 B)False

Which of the following could be a formula for the graph shown below?

Which of the following could be a formula for the graph shown below?

Simplify , if possible.

What are the zeros of $f(x)=x^{7}+4 x^{2}-3$ ? List them in ascending order separated by commas, and round any non-integer zeros to 3 decimal places.

Write a formula for a function, $f(x)$ , whose graph is identical to the graph of $y=x^{4}$ , except that the graph has holes at $(-3,81)$ and $(5,625)$ . Express the function $f(x)$ has a rational function.

Which of the following graphs show $p$ being proportional to the square of $q$ ?

Which of the following are rational functions:

If $f(x)=x^{2}-3$ and $g(x)=\frac{x^{4}}{2}-7$ , then $f(x)>g(x)$ on the interval ----------- (

What are the $x$ -intercepts, $y$ -intercepts, and horizontal asymptotes of the function $y=\frac{16 x^{2}-8 x-8}{x^{4}+8 x+32}$

It is possible for a rational function to have horizontal asymptotes at $y=2$ and $y=-6$ .

Which of the following could be a formula for the graph shown below?

The following figure gives the graphs of four power functions. Which one could be the graph of $y=1000 x^{-4}$ ? If none of the graphs match, enter "none".

The formula for the power function whose values are in the following table is $y=k x^{p}$ , where $k=$ --------- and $p=$ ----------- $The formula for the power function whose values are in the following table is y=k x^{p} , where k= --------- and p= -----------$

Determine the vertical and horizontal asymptotes, if they exist, of the function $y=3-\frac{13}{2 x+12}+\frac{1}{5 x^{4}}$

It is possible for a rational function $f$ to have no zeros, such that $f(x)<0$ for $x<5$ and $f(x)>0$ for $x>7$

Linear Functions and Change

Functions

Quadratic Functions

Exponential Functions

Logarithmic Functions

Transformations of Functions and Their Graphs

Trigonometry and Periodic Functions

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Exam 11: Polynomial and Rational Functions

Which of the following could be a formula for the graph shown below?

Which of the following could be a formula for the graph shown below?

Simplify , if possible.

What are the zeros of f(x)=x7+4x2−3f(x)=x^{7}+4 x^{2}-3f(x)=x7+4x2−3 ? List them in ascending order separated by commas, and round any non-integer zeros to 3 decimal places.

Write a formula for a function, f(x)f(x)f(x) , whose graph is identical to the graph of y=x4y=x^{4}y=x4 , except that the graph has holes at (−3,81)(-3,81)(−3,81) and (5,625)(5,625)(5,625) . Express the function f(x)f(x)f(x) has a rational function.

Which of the following graphs show ppp being proportional to the square of qqq ?

Which of the following are rational functions:

If f(x)=x2−3f(x)=x^{2}-3f(x)=x2−3 and g(x)=x42−7g(x)=\frac{x^{4}}{2}-7g(x)=2x4​−7 , then f(x)>g(x)f(x)>g(x)f(x)>g(x) on the interval ----------- (

What are the xxx -intercepts, yyy -intercepts, and horizontal asymptotes of the function y=16x2−8x−8x4+8x+32y=\frac{16 x^{2}-8 x-8}{x^{4}+8 x+32}y=x4+8x+3216x2−8x−8​

It is possible for a rational function to have horizontal asymptotes at y=2y=2y=2 and y=−6y=-6y=−6 .

The formula for the function graphed below has leading term axna x^{n}axn (i.e. f(x)=axn+f(x)=a x^{n}+f(x)=axn+ terms of lower degree). If nnn is as small as possible, then n=n=n= ---------- and a= ----------

Which of the following could be a formula for the graph shown below?

The following figure gives the graphs of four power functions. Which one could be the graph of y=1000x−4y=1000 x^{-4}y=1000x−4 ? If none of the graphs match, enter "none".

The formula for the power function whose values are in the following table is y=kxpy=k x^{p}y=kxp , where k=k=k= --------- and p=p=p= -----------

Determine the vertical and horizontal asymptotes, if they exist, of the function y=3−132x+12+15x4y=3-\frac{13}{2 x+12}+\frac{1}{5 x^{4}}y=3−2x+1213​+5x41​

The polynomial fff graphed below has leading term axna x^{n}axn (i.e. f(x)=axn+f(x)=a x^{n}+f(x)=axn+ terms of lower degree). We know that aaa is ----------- (positive \ negative), nnn is ------------- (even \ odd), and the smallest possible value of nnn is ----------------------.

It is possible for a rational function fff to have no zeros, such that f(x)<0f(x)<0f(x)<0 for x<5x<5x<5 and f(x)>0f(x)>0f(x)>0 for x>7x>7x>7

Linear Functions and Change

Functions

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

Vectors and Matrices

Sequences and Series

Parametric Equations and Conic Sections

Filters

What are the zeros of $f(x)=x^{7}+4 x^{2}-3$ ? List them in ascending order separated by commas, and round any non-integer zeros to 3 decimal places.

Write a formula for a function, $f(x)$ , whose graph is identical to the graph of $y=x^{4}$ , except that the graph has holes at $(-3,81)$ and $(5,625)$ . Express the function $f(x)$ has a rational function.

Which of the following graphs show $p$ being proportional to the square of $q$ ?

If $f(x)=x^{2}-3$ and $g(x)=\frac{x^{4}}{2}-7$ , then $f(x)>g(x)$ on the interval ----------- (

What are the $x$ -intercepts, $y$ -intercepts, and horizontal asymptotes of the function $y=\frac{16 x^{2}-8 x-8}{x^{4}+8 x+32}$

It is possible for a rational function to have horizontal asymptotes at $y=2$ and $y=-6$ .

The following figure gives the graphs of four power functions. Which one could be the graph of $y=1000 x^{-4}$ ? If none of the graphs match, enter "none".

The formula for the power function whose values are in the following table is $y=k x^{p}$ , where $k=$ --------- and $p=$ ----------- $The formula for the power function whose values are in the following table is y=k x^{p} , where k= --------- and p= -----------$

Determine the vertical and horizontal asymptotes, if they exist, of the function $y=3-\frac{13}{2 x+12}+\frac{1}{5 x^{4}}$

It is possible for a rational function $f$ to have no zeros, such that $f(x)<0$ for $x<5$ and $f(x)>0$ for $x>7$