Question 1

Find domain of the following function.​ $$g ( x ) = \frac { 1 } { x + 7 }$$ ​

Accepted Answer

A) all real numbers x except x = -7 
B) all real numbers x except x = 1 
C) all real numbers x except x = 49 
D) all real numbers x except x = 7 
E) all real numbers x except x = -1 
A) all real numbers x except x = -7 
B) all real numbers x except x = 1 
C) all real numbers x except x = 49 
D) all real numbers x except x = 7 
E) all real numbers x except x = -1 A

Question 2

Determine the zeros (if any)of the rational function $$f ( x ) = \frac { x ^ { 2 } - 4 } { x - 4 }$$ .

Accepted Answer

A) x = -4,x = 4 
B) no zeros 
C) x = -3 
D)  $$x = - \frac { 2 } { 3 } , x = \frac { 2 } { 3 }$$ 
E) x = -2,x = 2 
A) x = -4,x = 4 
B) no zeros 
C) x = -3 
D)  $$x = - \frac { 2 } { 3 } , x = \frac { 2 } { 3 }$$ 
E) x = -2,x = 2 E

Question 3

Determine the zeros (if any)of the rational function $f ( x ) = \frac { x ^ { 2 } - 81 } { x + 2 }$ .

Accepted Answer

A) x = -2 
B)  $x = - \frac { 9 } { 2 } , x = \frac { 9 } { 2 }$ 
C) x = -81,x = 81 
D) x = -9,x = 9 
E) no zeros 
A) x = -2 
B)  $x = - \frac { 9 } { 2 } , x = \frac { 9 } { 2 }$ 
C) x = -81,x = 81 
D) x = -9,x = 9 
E) no zeros D

Question 4

Find the zeros (if any)of the rational function.​ $$f ( x ) = 1 + \frac { 6 } { x ^ { 2 } - 7 }$$ ​

Accepted Answer

A) ±7 
B) ±6 
C) 6 
D) ±1 
E) ​7 
A) ±7 
B) ±6 
C) 6 
D) ±1 
E) ​7

Question 5

Determine the equations of any horizontal and vertical asymptotes of $$f ( x ) = \frac { x - 5 } { x ^ { 2 } - 25 }$$ .

Accepted Answer

A) horizontal: y = 0;vertical: x = -5 
B) horizontal: y = -5;vertical: x = 0 
C) horizontal: y = 5;vertical: x = -5 
D) horizontal: y = 0;vertical: x = 5 
E) horizontal: y = 0;vertical: none 
A) horizontal: y = 0;vertical: x = -5 
B) horizontal: y = -5;vertical: x = 0 
C) horizontal: y = 5;vertical: x = -5 
D) horizontal: y = 0;vertical: x = 5 
E) horizontal: y = 0;vertical: none

Question 6

The game commission introduces 100 deer into newly acquired state game lands.The population N of the herd is modeled by​ $N = \frac { 22 ( 5 + 3 t ) } { 1 + 0.04 t } , t \geq 0$ ​ where t is the time in years.
Select the correct graph of this model.
​

Accepted Answer

A) ​   
B) ​   
C) ​   
D) ​   
E) ​   
A) ​   
B) ​   
C) ​   
D) ​   
E) ​

Question 7

Find the domain of the function and identify any vertical and horizontal asymptotes.​ $$f ( x ) = \frac { x ^ { 3 } } { x ^ { 2 } - 49 }$$ ​

Accepted Answer

A) Domain: all real numbers x except x = 0 Vertical asymptote: x = ±7
Horizontal asymptote: No horizontal asymptote 
B) Domain: all real numbers x except x = ±7 Vertical asymptote: x = ±7
Horizontal asymptote: No horizontal asymptote 
C) Domain: all real numbers x except x = 7 Vertical asymptote: x = 7
Horizontal asymptote: y = 7 
D) Domain: all real numbers x Vertical asymptote: x = -7
Horizontal asymptote: y = 0 
E) Domain: all real numbers x except x = 0 Vertical asymptote: x = 0
Horizontal asymptote: y = -49 
A) Domain: all real numbers x except x = 0 Vertical asymptote: x = ±7
Horizontal asymptote: No horizontal asymptote 
B) Domain: all real numbers x except x = ±7 Vertical asymptote: x = ±7
Horizontal asymptote: No horizontal asymptote 
C) Domain: all real numbers x except x = 7 Vertical asymptote: x = 7
Horizontal asymptote: y = 7 
D) Domain: all real numbers x Vertical asymptote: x = -7
Horizontal asymptote: y = 0 
E) Domain: all real numbers x except x = 0 Vertical asymptote: x = 0
Horizontal asymptote: y = -49

Question 8

Find the zeros (if any)of the rational function.​ $$g ( x ) = \frac { x ^ { 3 } - 8 } { x ^ { 2 } + 1 }$$ ​

Accepted Answer

A) 8 
B) -8 
C) ​2 
D) -1 
E) -​2 
A) 8 
B) -8 
C) ​2 
D) -1 
E) -​2

Question 9

Determine the domain of the function $$f ( x ) = \frac { 5 } { ( x - 2 ) ^ { 4 } }$$ .

Accepted Answer

A) Domain: all real numbers except x = -5 and -2 
B) Domain: all real numbers 
C) Domain: all real numbers except x = -5 and 2 
D) Domain: all real numbers except x = 2 
E) Domain: all real numbers except x = 5 and 2 
A) Domain: all real numbers except x = -5 and -2 
B) Domain: all real numbers 
C) Domain: all real numbers except x = -5 and 2 
D) Domain: all real numbers except x = 2 
E) Domain: all real numbers except x = 5 and 2

Question 10

Determine the zeros (if any)of the rational function $$g ( x ) = 5 + \frac { 6 } { x ^ { 2 } + 5 }$$ .

Accepted Answer

A) no zeros 
B)  $x = - \sqrt { 5 } , x = \sqrt { 5 }$ 
C) ​x = -5,x = 5 
D) ​ $x = - \frac { 6 } { 5 } , x = \frac { 6 } { 5 }$ 
E) ​​x = -6 
A) no zeros 
B)  $x = - \sqrt { 5 } , x = \sqrt { 5 }$ 
C) ​x = -5,x = 5 
D) ​ $x = - \frac { 6 } { 5 } , x = \frac { 6 } { 5 }$ 
E) ​​x = -6

Question 11

Determine the equations of the vertical and horizontal asymptotes of the graph of the function $$f ( x ) = \frac { 5 x ^ { 2 } } { x ^ { 2 } - 4 }$$ .

Accepted Answer

A) horizontal: y = -2;vertical: x = 5 
B) horizontal: x = 2 and x = -2;vertical: y = -5 
C) horizontal: y = 5;vertical: x = 2 and x = -2 
D) horizontal: x = -5;vertical: y = 2 and y = -2 
E) horizontal: y = 5;vertical: x = 2 
A) horizontal: y = -2;vertical: x = 5 
B) horizontal: x = 2 and x = -2;vertical: y = -5 
C) horizontal: y = 5;vertical: x = 2 and x = -2 
D) horizontal: x = -5;vertical: y = 2 and y = -2 
E) horizontal: y = 5;vertical: x = 2

Question 12

Find the domain of $$f ( x ) = \frac { x ^ { 2 } - 25 } { x ^ { 2 } + 3 x - 40 }$$ .

Accepted Answer

A) all real numbers 
B) all real numbers except x = -8 
C) all real numbers except x = 5 and x = -8 
D) all real numbers except x = 8 and x = -5 
E) all real numbers except x = -5,x = 5 and x = -8 
A) all real numbers 
B) all real numbers except x = -8 
C) all real numbers except x = 5 and x = -8 
D) all real numbers except x = 8 and x = -5 
E) all real numbers except x = -5,x = 5 and x = -8

Question 13

Determine the equations of any horizontal and vertical asymptotes of $$f ( x ) = \frac { x ^ { 2 } - 9 } { x ^ { 2 } + x - 12 }$$ .

Accepted Answer

A) horizontal: y = 4;vertical: x = 0 
B) horizontal: y = 1;vertical: x = -4 
C) horizontal: y = 1;vertical: x = 3 and x = -4 
D) horizontal: y = -3;vertical: x = -4 
E) horizontal: y = 0;vertical: none 
A) horizontal: y = 4;vertical: x = 0 
B) horizontal: y = 1;vertical: x = -4 
C) horizontal: y = 1;vertical: x = 3 and x = -4 
D) horizontal: y = -3;vertical: x = -4 
E) horizontal: y = 0;vertical: none

Question 14

Identify all intercepts of $$f ( x ) = \frac { x ^ { 2 } } { x ^ { 2 } + 25 }$$ .

Accepted Answer

A) x-intercept: none;y-intercept: (0,6) 
B) x-intercept: none;y-intercept: (0,1) 
C) x-intercept: none;y-intercept: none 
D) x-intercept: (0,0);y-intercept: (0,0) 
E) x-intercepts: (-5,0)and (5,0);y-intercept: (0,1) 
A) x-intercept: none;y-intercept: (0,6) 
B) x-intercept: none;y-intercept: (0,1) 
C) x-intercept: none;y-intercept: none 
D) x-intercept: (0,0);y-intercept: (0,0) 
E) x-intercepts: (-5,0)and (5,0);y-intercept: (0,1)

Question 15

Given $f ( x ) = \frac { x ^ { 2 } + 49 } { x + 7 } , g ( x ) = x - 7$ .Determine the domains of f(x)and g(x). ​

Accepted Answer

A) Domain of f(x): all real numbers except -7 Domain of g(x): all real numbers except 7 
B) Domain of f(x): all real numbers Domain of g(x): all real numbers except 7 
C) Domain of f(x): all real numbers Domain of g(x): all real numbers 
D) Domain of f(x): all real numbers except -7 Domain of g(x): all real numbers 
E) Domain of f(x): all real numbers except 7 Domain of g(x): all real numbers 
A) Domain of f(x): all real numbers except -7 Domain of g(x): all real numbers except 7 
B) Domain of f(x): all real numbers Domain of g(x): all real numbers except 7 
C) Domain of f(x): all real numbers Domain of g(x): all real numbers 
D) Domain of f(x): all real numbers except -7 Domain of g(x): all real numbers 
E) Domain of f(x): all real numbers except 7 Domain of g(x): all real numbers

Question 16

Given $f ( x ) = \frac { x ^ { 2 } - 36 } { x + 6 } , g ( x ) = x - 6$ .Complete the table and explain how the two functions differ. $$\begin{array} { | c | c | c | c | c | c | c | c | } 
\hline x & - 8 & - 7.5 & - 7 & - 6.5 & - 6 & - 5.5 & - 5 \
\hline f ( x ) & & & & & & & \
\hline g ( x ) & & & & & & & \
\hline
\end{array}$$

Accepted Answer

A) ​ $$\begin{array} { | c | c | c | c | c | c | c | c | } 
\hline x & - 8 & - 7.5 & - 7 & - 6.5 & - 6 & - 5.5 & - 5 \
\hline f ( x ) & - 14 & - 13.5 & \text { Undefined } & - 12.5 & - 12 & - 11.5 & - 11 \
\hline g ( x ) & - 14 & - 13.5 & - 13 & - 12.5 & - 12 & - 11.5 & - 11 \
\hline
\end{array}$$
The graph of f(x)= g(x)except when x = -7.Because the factor x + 6 canceled,there is a hole in the graph of f(x)when x = -7.​ 
B) ​ $$\begin{array} { | c | c | c | c | c | c | c | c | } 
\hline x & - 8 & - 7.5 & - 7 & - 6.5 & - 6 & - 5.5 & - 5 \
\hline f ( x ) & - 14 & \text { Undefined } & - 13 & - 12.5 & - 12 & - 11.5 & - 11 \
\hline g ( x ) & - 14 & - 13.5 & - 13 & - 12.5 & - 12 & - 11.5 & - 11 \
\hline
\end{array}$$
​The graph of f(x)= g(x)except when x = -7.5.Because the factor x + 6 canceled,there is a hole in the graph of f(x)when x = -7.5.​ 
C) ​ $$\begin{array} { | c | c | c | c | c | c | c | c | } 
\hline x & - 8 & - 7.5 & - 7 & - 6.5 & - 6 & - 5.5 & - 5 \
\hline f ( x ) & - 14 & - 13.5 & - 13 & \text { Undefined } & - 12 & - 11.5 & - 11 \
\hline g ( x ) & - 14 & - 13.5 & - 13 & - 12.5 & - 12 & - 11.5 & - 11 \
\hline
\end{array}$$
The graph of f(x)= g(x)except when x = -6.5.Because the factor x + 6 canceled,there is a hole in the graph of f(x)when x = -6.5. 
D) ​ $$\begin{array} { | c | c | c | c | c | c | c | c | } 
\hline x & - 8 & - 7.5 & - 7 & - 6.5 & - 6 & - 5.5 & - 5 \
\hline f ( x ) & - 14 & - 13.5 & - 13 & - 12.5 & \text { Undefined } & - 11.5 & - 11 \
\hline g ( x ) & - 14 & - 13.5 & - 13 & - 12.5 & - 12 & - 11.5 & - 11 \
\hline
\end{array}$$
The graph of f(x)= g(x)except when x = -6.Because the factor x + 6 canceled,there is a hole in the graph of f(x)when x = -6.​ 
E) ​ $$\begin{array} { | c | c | c | c | c | c | c | c | } 
\hline x & - 8 & - 7.5 & - 7 & - 6.5 & - 6 & - 5.5 & - 5 \
\hline f ( x ) & - 14 & - 13.5 & - 13 & - 12.5 & - 12 & \text { Undefined } & - 11 \
\hline g ( x ) & - 14 & - 13.5 & - 13 & - 12.5 & - 12 & - 11.5 & - 11 \
\hline
\end{array}$$
​The graph of f(x)= g(x)except when x = -5.5.Because the factor x + 6 canceled,there is a hole in the graph f(x)when x = -5.5.​ 
A) ​ $$\begin{array} { | c | c | c | c | c | c | c | c | } 
\hline x & - 8 & - 7.5 & - 7 & - 6.5 & - 6 & - 5.5 & - 5 \
\hline f ( x ) & - 14 & - 13.5 & \text { Undefined } & - 12.5 & - 12 & - 11.5 & - 11 \
\hline g ( x ) & - 14 & - 13.5 & - 13 & - 12.5 & - 12 & - 11.5 & - 11 \
\hline
\end{array}$$
The graph of f(x)= g(x)except when x = -7.Because the factor x + 6 canceled,there is a hole in the graph of f(x)when x = -7.​ 
B) ​ $$\begin{array} { | c | c | c | c | c | c | c | c | } 
\hline x & - 8 & - 7.5 & - 7 & - 6.5 & - 6 & - 5.5 & - 5 \
\hline f ( x ) & - 14 & \text { Undefined } & - 13 & - 12.5 & - 12 & - 11.5 & - 11 \
\hline g ( x ) & - 14 & - 13.5 & - 13 & - 12.5 & - 12 & - 11.5 & - 11 \
\hline
\end{array}$$
​The graph of f(x)= g(x)except when x = -7.5.Because the factor x + 6 canceled,there is a hole in the graph of f(x)when x = -7.5.​ 
C) ​ $$\begin{array} { | c | c | c | c | c | c | c | c | } 
\hline x & - 8 & - 7.5 & - 7 & - 6.5 & - 6 & - 5.5 & - 5 \
\hline f ( x ) & - 14 & - 13.5 & - 13 & \text { Undefined } & - 12 & - 11.5 & - 11 \
\hline g ( x ) & - 14 & - 13.5 & - 13 & - 12.5 & - 12 & - 11.5 & - 11 \
\hline
\end{array}$$
The graph of f(x)= g(x)except when x = -6.5.Because the factor x + 6 canceled,there is a hole in the graph of f(x)when x = -6.5. 
D) ​ $$\begin{array} { | c | c | c | c | c | c | c | c | } 
\hline x & - 8 & - 7.5 & - 7 & - 6.5 & - 6 & - 5.5 & - 5 \
\hline f ( x ) & - 14 & - 13.5 & - 13 & - 12.5 & \text { Undefined } & - 11.5 & - 11 \
\hline g ( x ) & - 14 & - 13.5 & - 13 & - 12.5 & - 12 & - 11.5 & - 11 \
\hline
\end{array}$$
The graph of f(x)= g(x)except when x = -6.Because the factor x + 6 canceled,there is a hole in the graph of f(x)when x = -6.​ 
E) ​ $$\begin{array} { | c | c | c | c | c | c | c | c | } 
\hline x & - 8 & - 7.5 & - 7 & - 6.5 & - 6 & - 5.5 & - 5 \
\hline f ( x ) & - 14 & - 13.5 & - 13 & - 12.5 & - 12 & \text { Undefined } & - 11 \
\hline g ( x ) & - 14 & - 13.5 & - 13 & - 12.5 & - 12 & - 11.5 & - 11 \
\hline
\end{array}$$
​The graph of f(x)= g(x)except when x = -5.5.Because the factor x + 6 canceled,there is a hole in the graph f(x)when x = -5.5.​

Question 17

Determine the equations of the vertical and horizontal asymptotes of the graph of the function $$f ( x ) = \frac { 1 } { x - 5 }$$ .

Accepted Answer

A) horizontal: y = 1;vertical: x = 5 
B) horizontal: x = 0;vertical: y = 5​ 
C) horizontal: y = -5;vertical: x = 0 
D) horizontal: x = 5;vertical: y = -1 
E) horizontal: y = 0;vertical: x = 5 
A) horizontal: y = 1;vertical: x = 5 
B) horizontal: x = 0;vertical: y = 5​ 
C) horizontal: y = -5;vertical: x = 0 
D) horizontal: x = 5;vertical: y = -1 
E) horizontal: y = 0;vertical: x = 5

Question 18

Find the domain of $$f ( x ) = \frac { x + 2 } { x ^ { 2 } - 4 }$$ .

Accepted Answer

A) all real numbers except x = -2 
B) all real numbers 
C) all real numbers except x = -2 and x = 2 
D) all real numbers except x = 4 
E) all real numbers except x = 2 
A) all real numbers except x = -2 
B) all real numbers 
C) all real numbers except x = -2 and x = 2 
D) all real numbers except x = 4 
E) all real numbers except x = 2

Question 19

The cost C (in millions of dollars)of removing p% of the industrial and municipal pollutants discharged into a river is given by​ $C = \frac { 235 p } { 100 - p } , 0 \leq p < 100$ .
​
According to this model,would it be possible to remove 100% of the pollutants? Explain.
​

Accepted Answer

A) No.The function is undefined at p = 100. 
B) Yes 
A) No.The function is undefined at p = 100. 
B) Yes

Question 20

Find the zeros (if any)of the rational function.​ $$f ( x ) = 2 + \frac { 12 } { x ^ { 2 } + 2 }$$ ​

Accepted Answer

A) -2 
B) 2 
C) 8 
D) -8 
E) None 
A) -2 
B) 2 
C) 8 
D) -8 
E) None

Exam 16: Rational Functions

Find domain of the following function.​ g(x)=1x+7g ( x ) = \frac { 1 } { x + 7 }g(x)=x+71​ ​

Determine the zeros (if any)of the rational function f(x)=x2−4x−4f ( x ) = \frac { x ^ { 2 } - 4 } { x - 4 }f(x)=x−4x2−4​ .

Determine the zeros (if any)of the rational function f(x)=x2−81x+2f ( x ) = \frac { x ^ { 2 } - 81 } { x + 2 }f(x)=x+2x2−81​ .

Find the zeros (if any)of the rational function.​ f(x)=1+6x2−7f ( x ) = 1 + \frac { 6 } { x ^ { 2 } - 7 }f(x)=1+x2−76​ ​

Determine the equations of any horizontal and vertical asymptotes of f(x)=x−5x2−25f ( x ) = \frac { x - 5 } { x ^ { 2 } - 25 }f(x)=x2−25x−5​ .

Find the domain of the function and identify any vertical and horizontal asymptotes.​ f(x)=x3x2−49f ( x ) = \frac { x ^ { 3 } } { x ^ { 2 } - 49 }f(x)=x2−49x3​ ​

Find the zeros (if any)of the rational function.​ g(x)=x3−8x2+1g ( x ) = \frac { x ^ { 3 } - 8 } { x ^ { 2 } + 1 }g(x)=x2+1x3−8​ ​

Determine the domain of the function f(x)=5(x−2)4f ( x ) = \frac { 5 } { ( x - 2 ) ^ { 4 } }f(x)=(x−2)45​ .

Determine the zeros (if any)of the rational function g(x)=5+6x2+5g ( x ) = 5 + \frac { 6 } { x ^ { 2 } + 5 }g(x)=5+x2+56​ .

Determine the equations of the vertical and horizontal asymptotes of the graph of the function f(x)=5x2x2−4f ( x ) = \frac { 5 x ^ { 2 } } { x ^ { 2 } - 4 }f(x)=x2−45x2​ .

Find the domain of f(x)=x2−25x2+3x−40f ( x ) = \frac { x ^ { 2 } - 25 } { x ^ { 2 } + 3 x - 40 }f(x)=x2+3x−40x2−25​ .

Determine the equations of any horizontal and vertical asymptotes of f(x)=x2−9x2+x−12f ( x ) = \frac { x ^ { 2 } - 9 } { x ^ { 2 } + x - 12 }f(x)=x2+x−12x2−9​ .

Identify all intercepts of f(x)=x2x2+25f ( x ) = \frac { x ^ { 2 } } { x ^ { 2 } + 25 }f(x)=x2+25x2​ .

Given f(x)=x2+49x+7,g(x)=x−7f ( x ) = \frac { x ^ { 2 } + 49 } { x + 7 } , g ( x ) = x - 7f(x)=x+7x2+49​,g(x)=x−7 .Determine the domains of f(x)and g(x). ​

Given f(x)=x2−36x+6,g(x)=x−6f ( x ) = \frac { x ^ { 2 } - 36 } { x + 6 } , g ( x ) = x - 6f(x)=x+6x2−36​,g(x)=x−6 .Complete the table and explain how the two functions differ. x -8 -7.5 -7 -6.5 -6 -5.5 -5 f(x) g(x)

Determine the equations of the vertical and horizontal asymptotes of the graph of the function f(x)=1x−5f ( x ) = \frac { 1 } { x - 5 }f(x)=x−51​ .

Find the domain of f(x)=x+2x2−4f ( x ) = \frac { x + 2 } { x ^ { 2 } - 4 }f(x)=x2−4x+2​ .

Find the zeros (if any)of the rational function.​ f(x)=2+12x2+2f ( x ) = 2 + \frac { 12 } { x ^ { 2 } + 2 }f(x)=2+x2+212​ ​

Rectangular Coordinates

Graphs of Equations

Linear Equations in Two Variables

Functions

Analyzing Graphs of Functions

A Library of Parent Functions

Transformations of Functions

Combinations of Functions Composite Functions

Inverse Functions

Mathematical Modeling and Variation

Quadratic Functions and Models

Polynomial Functions of Higher Degree

Polynomial and Synthetic Division

Complex Numbers

Zeros of Polynomial Functions

Nonlinear Inequalities

Exponential Functions and Their Graphs

Logarithmic Functions and Their Graphs

Properties of Logarithms

Exponential and Logarithmic Equations

Exponential and Logarithmic Models

Radian and Degree Measure

Trigonometric Functions The Unit Circle

Right Triangle Trigonometry

Trigonometric Functions of Any Angle

Graphs of Sine and Cosine Functions

Graphs of Other Trigonometric Functions

Inverse Trigonometric Functions

Applications and Models

Using Fundamental Identities

Verifying Trigonometric Equations

Solving Trigonometric Equations

Sum and Difference Formulas

Multiple Angle and Product to Sum Formulas

Law of Sines

Law of Cosines

Vectors in the Plane

Vectors and Dot Products

Trigonometric Form of a Complex Number

Linear and Nonlinear Systems of Equations

Two Variable Linear Systems

Multivariable Linear Systems

Partial Fractions

Systems of Inequalities

Linear Programming

Matrices and Systems of Equations

Operations With Matrices

The Inverse of a Square Matrix

The Determinant of a Square Matrix

Applications of Matrices and Determinants

Sequences and Series

Arithmetic Sequences and Partial Sums

Geometric Sequences and Series

Mathematical Induction

The Binomial Theorem

Counting Principles

Probability

Lines

Introduction to Conics Parabolas

Ellipses

Hyperbolas

Find domain of the following function. $g ( x ) = \frac { 1 } { x + 7 }$

Determine the zeros (if any)of the rational function $f ( x ) = \frac { x ^ { 2 } - 4 } { x - 4 }$ .

Determine the zeros (if any)of the rational function $f ( x ) = \frac { x ^ { 2 } - 81 } { x + 2 }$ .

Find the zeros (if any)of the rational function. $f ( x ) = 1 + \frac { 6 } { x ^ { 2 } - 7 }$

Determine the equations of any horizontal and vertical asymptotes of $f ( x ) = \frac { x - 5 } { x ^ { 2 } - 25 }$ .

Find the domain of the function and identify any vertical and horizontal asymptotes. $f ( x ) = \frac { x ^ { 3 } } { x ^ { 2 } - 49 }$

Find the zeros (if any)of the rational function. $g ( x ) = \frac { x ^ { 3 } - 8 } { x ^ { 2 } + 1 }$

Determine the domain of the function $f ( x ) = \frac { 5 } { ( x - 2 ) ^ { 4 } }$ .

Determine the zeros (if any)of the rational function $g ( x ) = 5 + \frac { 6 } { x ^ { 2 } + 5 }$ .

Determine the equations of the vertical and horizontal asymptotes of the graph of the function $f ( x ) = \frac { 5 x ^ { 2 } } { x ^ { 2 } - 4 }$ .

Find the domain of $f ( x ) = \frac { x ^ { 2 } - 25 } { x ^ { 2 } + 3 x - 40 }$ .

Determine the equations of any horizontal and vertical asymptotes of $f ( x ) = \frac { x ^ { 2 } - 9 } { x ^ { 2 } + x - 12 }$ .

Identify all intercepts of $f ( x ) = \frac { x ^ { 2 } } { x ^ { 2 } + 25 }$ .

Given $f ( x ) = \frac { x ^ { 2 } + 49 } { x + 7 } , g ( x ) = x - 7$ .Determine the domains of f(x)and g(x).

Given $f ( x ) = \frac { x ^ { 2 } - 36 } { x + 6 } , g ( x ) = x - 6$ .Complete the table and explain how the two functions differ. x -8 -7.5 -7 -6.5 -6 -5.5 -5 f(x) g(x)

Determine the equations of the vertical and horizontal asymptotes of the graph of the function $f ( x ) = \frac { 1 } { x - 5 }$ .

Find the domain of $f ( x ) = \frac { x + 2 } { x ^ { 2 } - 4 }$ .

Find the zeros (if any)of the rational function. $f ( x ) = 2 + \frac { 12 } { x ^ { 2 } + 2 }$