Question 1

Given $$f ( x ) = \frac { x ^ { 2 } - 16 } { x + 4 } , g ( x ) = x - 4$$ .Complete the table and explain how the two functions differ. $$\begin{array} { | c | c | c | c | c | c | c | c | } 
\hline x & - 6 & - 5.5 & - 5 & - 4.5 & - 4 & - 3.5 & - 3 \
\hline f ( x ) & & & & & & & \
\hline g ( x ) & & & & & & & \
\hline
\end{array}$$
​

Accepted Answer

A) ​$$\begin{array} { | c | c | c | c | c | c | c | c | } 
\hline x & - 6 & - 5.5 & - 5 & - 4.5 & - 4 & - 3.5 & - 3 \
\hline f ( x ) & - 10 & - 9.5 & - 9 & - 8.5 & \text { Undefined } & - 7.5 & - 7 \
\hline g ( x ) & - 10 & - 9.5 & - 9 & - 8.5 & - 8 & - 7.5 & - 7 \
\hline
\end{array}$$ The graph of f(x)= g(x)except when x = -4.Because the factor x + 4 canceled,there is a hole in the graph of f(x)when x = -4. 
B) ​ $$\begin{array} { | c | c | c | c | c | c | c | c | } 
\hline x & - 6 & - 5.5 & - 5 & - 4.5 & - 4 & - 3.5 & - 3 \
\hline f ( x ) & - 10 & - 9.5 & - 9 & - 8.5 & - 8 & \text { Undefined } & - 7 \
\hline g ( x ) & - 10 & - 9.5 & - 9 & - 8.5 & - 8 & - 7.5 & - 7 \
\hline
\end{array}$$
The graph of f(x)= g(x)except when x = -3.5.Because the factor x + 4 canceled,there is a hole in the graph of f(x)when x = -3.5. 
C) ​ $$\begin{array} { | c | c | c | c | c | c | c | c | } 
\hline x & - 6 & - 5.5 & - 5 & - 4.5 & - 4 & - 3.5 & - 3 \
\hline f ( x ) & - 10 & - 9.5 & - 9 & \text { Undefined } & - 8 & - 7.5 & - 7 \
\hline g ( x ) & - 10 & - 9.5 & - 9 & - 8.5 & - 8 & - 7.5 & - 7 \
\hline
\end{array}$$
The graph of f(x)= g(x)except when x = -4.5.Because the factor x + 4 canceled,there is a hole in the graph of f(x)when x = -4.5. 
D) ​ $$\begin{array} { | c | c | c | c | c | c | c | c | } 
\hline x & - 6 & - 5.5 & - 5 & - 4.5 & - 4 & - 3.5 & - 3 \
\hline f ( x ) & - 10 & - 9.5 & \text { Undefined } & - 8.5 & - 8 & - 7.5 & - 7 \
\hline g ( x ) & - 10 & - 9.5 & - 9 & - 8.5 & - 8 & - 7.5 & - 7 \
\hline
\end{array}$$
The graph of f(x)= g(x)except when x = -5.Because the factor x + 4 canceled,there is a hole in the graph of f(x)when x = -5. 
E) ​ $$\begin{array} { | c | c | c | c | c | c | c | c | } 
\hline x & - 6 & - 5.5 & - 5 & - 4.5 & - 4 & - 3.5 & - 3 \
\hline f ( x ) & - 10 & \text { Undefined } & - 9 & - 8.5 & - 8 & - 7.5 & - 7 \
\hline g ( x ) & - 10 & - 9.5 & - 9 & - 8.5 & - 8 & - 7.5 & - 7 \
\hline
\end{array}$$
The graph of f(x)= g(x)except when x = -5.5.Because the factor x + 4 canceled,there is a hole in the graph of f(x)when x = -5.5.​ 
A) ​$$\begin{array} { | c | c | c | c | c | c | c | c | } 
\hline x & - 6 & - 5.5 & - 5 & - 4.5 & - 4 & - 3.5 & - 3 \
\hline f ( x ) & - 10 & - 9.5 & - 9 & - 8.5 & \text { Undefined } & - 7.5 & - 7 \
\hline g ( x ) & - 10 & - 9.5 & - 9 & - 8.5 & - 8 & - 7.5 & - 7 \
\hline
\end{array}$$ The graph of f(x)= g(x)except when x = -4.Because the factor x + 4 canceled,there is a hole in the graph of f(x)when x = -4. 
B) ​ $$\begin{array} { | c | c | c | c | c | c | c | c | } 
\hline x & - 6 & - 5.5 & - 5 & - 4.5 & - 4 & - 3.5 & - 3 \
\hline f ( x ) & - 10 & - 9.5 & - 9 & - 8.5 & - 8 & \text { Undefined } & - 7 \
\hline g ( x ) & - 10 & - 9.5 & - 9 & - 8.5 & - 8 & - 7.5 & - 7 \
\hline
\end{array}$$
The graph of f(x)= g(x)except when x = -3.5.Because the factor x + 4 canceled,there is a hole in the graph of f(x)when x = -3.5. 
C) ​ $$\begin{array} { | c | c | c | c | c | c | c | c | } 
\hline x & - 6 & - 5.5 & - 5 & - 4.5 & - 4 & - 3.5 & - 3 \
\hline f ( x ) & - 10 & - 9.5 & - 9 & \text { Undefined } & - 8 & - 7.5 & - 7 \
\hline g ( x ) & - 10 & - 9.5 & - 9 & - 8.5 & - 8 & - 7.5 & - 7 \
\hline
\end{array}$$
The graph of f(x)= g(x)except when x = -4.5.Because the factor x + 4 canceled,there is a hole in the graph of f(x)when x = -4.5. 
D) ​ $$\begin{array} { | c | c | c | c | c | c | c | c | } 
\hline x & - 6 & - 5.5 & - 5 & - 4.5 & - 4 & - 3.5 & - 3 \
\hline f ( x ) & - 10 & - 9.5 & \text { Undefined } & - 8.5 & - 8 & - 7.5 & - 7 \
\hline g ( x ) & - 10 & - 9.5 & - 9 & - 8.5 & - 8 & - 7.5 & - 7 \
\hline
\end{array}$$
The graph of f(x)= g(x)except when x = -5.Because the factor x + 4 canceled,there is a hole in the graph of f(x)when x = -5. 
E) ​ $$\begin{array} { | c | c | c | c | c | c | c | c | } 
\hline x & - 6 & - 5.5 & - 5 & - 4.5 & - 4 & - 3.5 & - 3 \
\hline f ( x ) & - 10 & \text { Undefined } & - 9 & - 8.5 & - 8 & - 7.5 & - 7 \
\hline g ( x ) & - 10 & - 9.5 & - 9 & - 8.5 & - 8 & - 7.5 & - 7 \
\hline
\end{array}$$
The graph of f(x)= g(x)except when x = -5.5.Because the factor x + 4 canceled,there is a hole in the graph of f(x)when x = -5.5.​

Question 2

Determine the zeros (if any)of the rational function $$f ( x ) = \frac { x ^ { 2 } - 4 } { x + 3 }$$ .

Accepted Answer

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

Question 3

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

Accepted Answer

A) Domain: all real numbers x except x = 0 Vertical asymptote: x = 0
Horizontal asymptote: y = -2 
B) Domain: all real numbers x except x = -3 Vertical asymptote: x = -3
Horizontal asymptote: No horizontal asymptote 
C) Domain: all real numbers x except x = 3 Vertical asymptote: x = 3
Horizontal asymptote: No horizontal asymptote 
D) Domain: all real numbers x except x = 3 Vertical asymptote: x = 3
Horizontal asymptote: y = 2 
E) Domain: all real numbers x Vertical asymptote: x = -3
Horizontal asymptote: y = 0 
A) Domain: all real numbers x except x = 0 Vertical asymptote: x = 0
Horizontal asymptote: y = -2 
B) Domain: all real numbers x except x = -3 Vertical asymptote: x = -3
Horizontal asymptote: No horizontal asymptote 
C) Domain: all real numbers x except x = 3 Vertical asymptote: x = 3
Horizontal asymptote: No horizontal asymptote 
D) Domain: all real numbers x except x = 3 Vertical asymptote: x = 3
Horizontal asymptote: y = 2 
E) Domain: all real numbers x Vertical asymptote: x = -3
Horizontal asymptote: y = 0

Question 4

Select the graph of the rational function $$f ( x ) = - \frac { x + 6 } { x + 7 }$$ . ​

Accepted Answer

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

Question 5

Determine the domain of $$f ( x ) = \frac { 6 x + 6 } { x ^ { 2 } - 6 x }$$ .

Accepted Answer

A) all real numbers except x = 0 and x = 6 
B) all real numbers 
C) all real numbers except x = 6 
D) all real numbers except x = -6 and x = -1 
E) all real numbers except x = -1,x = 0 and x = 6 
A) all real numbers except x = 0 and x = 6 
B) all real numbers 
C) all real numbers except x = 6 
D) all real numbers except x = -6 and x = -1 
E) all real numbers except x = -1,x = 0 and x = 6

Question 6

Find domain of the following function. $$g ( x ) = \frac { x ^ { 2 } - 4 } { x ^ { 2 } - 3 x + 2 }$$ ​

Accepted Answer

A) all real numbers x except x = -4 and x = -1 
B) all real numbers x except x = -3 and x = 2 
C) all real numbers x except x = 3 and x = 4 
D) all real numbers x except x = 2 and x = 1 
E) all real numbers x except x = -2 and x = 1 
A) all real numbers x except x = -4 and x = -1 
B) all real numbers x except x = -3 and x = 2 
C) all real numbers x except x = 3 and x = 4 
D) all real numbers x except x = 2 and x = 1 
E) all real numbers x except x = -2 and x = 1

Question 7

Determine the domain of the function $$f ( x ) = \frac { x ^ { 2 } - 9 } { x ^ { 2 } + 4 x + 3 }$$ .

Accepted Answer

A) Domain: all real numbers except x = -3 and 1 
B) Domain: all real numbers except x = 1 
C) Domain: all real numbers except x = -3 and -1 
D) Domain: all real numbers except x = 3 and 1 
E) Domain: all real numbers 
A) Domain: all real numbers except x = -3 and 1 
B) Domain: all real numbers except x = 1 
C) Domain: all real numbers except x = -3 and -1 
D) Domain: all real numbers except x = 3 and 1 
E) Domain: all real numbers

Question 8

Determine the zeros (if any)of the rational function $$g ( x ) = \frac { x ^ { 3 } - 8 } { x ^ { 2 } + 6 }$$ .

Accepted Answer

A) x = -2,x = 2 
B) x = 2 
C)  $x = - \sqrt { 6 } , x = \sqrt { 6 } , x = 2$ 
D)  $x = - \sqrt { 6 } , x = \sqrt { 6 } , x = - 2 , x = 2$ 
E) no zeros 
A) x = -2,x = 2 
B) x = 2 
C)  $x = - \sqrt { 6 } , x = \sqrt { 6 } , x = 2$ 
D)  $x = - \sqrt { 6 } , x = \sqrt { 6 } , x = - 2 , x = 2$ 
E) no zeros

Question 9

Find all intercepts of the following function.​ $f ( x ) = \frac { 4 x ^ { 2 } - 6 x + 6 } { x - 4 }$ ​

Accepted Answer

A) y-intercept: $$\left( 0 , - \frac { 3 } { 2 } \right)$$ 
B) y-intercept: $\left( \frac { 3 } { 2 } , 0 \right)$ 
C) y-intercept: (0,3) 
D) Intercept: (0,0) 
E) x-intercept: $\left( - \frac { 3 } { 2 } , 0 \right)$ 
A) y-intercept: $$\left( 0 , - \frac { 3 } { 2 } \right)$$ 
B) y-intercept: $\left( \frac { 3 } { 2 } , 0 \right)$ 
C) y-intercept: (0,3) 
D) Intercept: (0,0) 
E) x-intercept: $\left( - \frac { 3 } { 2 } , 0 \right)$

Question 10

Select the correct graph of the following function.​ $$f ( x ) = \frac { x ^ { 2 } - 16 } { x + 4 }$$ ​ ​

Accepted Answer

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

Question 11

Simplify f(x)and find any vertical asymptotes. ​​ $$f ( x ) = \frac { x ^ { 2 } - 4 } { x + 2 }$$ ​

Accepted Answer

A) f(x)= -x + 2;no vertical asymptotes 
B) f(x)= x;no vertical asymptotes 
C) f(x)= -x - 2;no vertical asymptotes 
D) f(x)= x - 2;no vertical asymptotes 
E) f(x)= x + 2;no vertical asymptotes 
A) f(x)= -x + 2;no vertical asymptotes 
B) f(x)= x;no vertical asymptotes 
C) f(x)= -x - 2;no vertical asymptotes 
D) f(x)= x - 2;no vertical asymptotes 
E) f(x)= x + 2;no vertical asymptotes

Question 12

Find the domain of the function and identify any vertical and horizontal asymptotes.​ $$f ( x ) = \frac { 9 } { ( x - 3 ) ^ { 3 } }$$ ​

Accepted Answer

A) Domain: all real numbers x Vertical asymptote: x = 0
Horizontal asymptote: y = 0 
B) Domain: all real numbers x except x = 9 Vertical asymptote: x = 0
Horizontal asymptote: y = 0 
C) Domain: all real numbers x except x = 3 Vertical asymptote: x = 0
Horizontal asymptote: y = 9 
D) Domain: all real numbers x Vertical asymptote: x = 0
Horizontal asymptote: y = 9 
E) Domain: all real numbers x except x = 3 Vertical asymptote: x = 3
Horizontal asymptote: y = 0 
A) Domain: all real numbers x Vertical asymptote: x = 0
Horizontal asymptote: y = 0 
B) Domain: all real numbers x except x = 9 Vertical asymptote: x = 0
Horizontal asymptote: y = 0 
C) Domain: all real numbers x except x = 3 Vertical asymptote: x = 0
Horizontal asymptote: y = 9 
D) Domain: all real numbers x Vertical asymptote: x = 0
Horizontal asymptote: y = 9 
E) Domain: all real numbers x except x = 3 Vertical asymptote: x = 3
Horizontal asymptote: y = 0

Question 13

Select the correct graph for the following rational function.​ $$f ( x ) = \frac { 11 } { x - 8 }$$ ​

Accepted Answer

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

Question 14

Find the domain of the function and identify any vertical and horizontal asymptotes.​ $$f ( x ) = \frac { 25 } { x ^ { 2 } }$$ ​

Accepted Answer

A) Domain: all real numbers x except x = 0 Vertical asymptote: x = 0
Horizontal asymptote: y = 0 
B) ​Domain: all real numbers x except x = 5 Vertical asymptote: x = 0
Horizontal asymptote: y = 0 
C) ​Domain: all real numbers x except x = 25 Vertical asymptote: x = 0
Horizontal asymptote: y = 0​ 
D) ​Domain: all real numbers x Vertical asymptote: x = 0
Horizontal asymptote: y = 0​ 
E) ​Domain: all real numbers x except x = ±5 Vertical asymptote: y = 0
Horizontal asymptote: x = 0​ 
A) Domain: all real numbers x except x = 0 Vertical asymptote: x = 0
Horizontal asymptote: y = 0 
B) ​Domain: all real numbers x except x = 5 Vertical asymptote: x = 0
Horizontal asymptote: y = 0 
C) ​Domain: all real numbers x except x = 25 Vertical asymptote: x = 0
Horizontal asymptote: y = 0​ 
D) ​Domain: all real numbers x Vertical asymptote: x = 0
Horizontal asymptote: y = 0​ 
E) ​Domain: all real numbers x except x = ±5 Vertical asymptote: y = 0
Horizontal asymptote: x = 0​

Question 15

Find vertical and horizontal asymptotes.​ $$f ( x ) = \frac { 9 + 6 x } { 6 + x }$$ ​

Accepted Answer

A) Vertical asymptote: x = -6 Horizontal asymptote: y = 6 
B) Vertical asymptote: x = 0 Horizontal asymptote: y = -6 
C) Vertical asymptote: x = 6 Horizontal asymptote: y = -6 
D) Vertical asymptote: x = 0 Horizontal asymptote: y = 6 
E) Vertical asymptote: x = -6 Horizontal asymptote: y = 0 
A) Vertical asymptote: x = -6 Horizontal asymptote: y = 6 
B) Vertical asymptote: x = 0 Horizontal asymptote: y = -6 
C) Vertical asymptote: x = 6 Horizontal asymptote: y = -6 
D) Vertical asymptote: x = 0 Horizontal asymptote: y = 6 
E) Vertical asymptote: x = -6 Horizontal asymptote: y = 0

Question 16

Select the correct rational function for the following graph.​   ​

Accepted Answer

A)  $$f ( x ) = \frac { 3 } { x - 4 }$$ 
B)  $f ( x ) = \frac { 3 } { x + 4 }$ 
C)  $$f ( x ) = \frac { 3 } { x + 3 }$$ 
D) ​ $f ( x ) = \frac { 4 } { x - 3 }$ 
E) ​ $f ( x ) = \frac { 4 } { x - 4 }$ 
A)  $$f ( x ) = \frac { 3 } { x - 4 }$$ 
B)  $f ( x ) = \frac { 3 } { x + 4 }$ 
C)  $$f ( x ) = \frac { 3 } { x + 3 }$$ 
D) ​ $f ( x ) = \frac { 4 } { x - 3 }$ 
E) ​ $f ( x ) = \frac { 4 } { x - 4 }$

Question 17

Find all intercepts of the following function.​ $$g ( x ) = \frac { 1 } { x - 4 }$$ ​

Accepted Answer

A) y-intercept: $$\left( 0 , \frac { 1 } { 4 } \right)$$ 
B) x-intercept: $\left( - \frac { 1 } { 4 } , 0 \right)$ 
C) y-intercept: $\left( 0 , - \frac { 1 } { 4 } \right)$ 
D) x-intercept: $\left( \frac { 1 } { 4 } , 0 \right)$ 
E) x-intercept: $\left( - \frac { 1 } { 4 } , 0 \right)$ and y-intercept: $\left( 0 , - \frac { 1 } { 4 } \right)$ 
A) y-intercept: $$\left( 0 , \frac { 1 } { 4 } \right)$$ 
B) x-intercept: $\left( - \frac { 1 } { 4 } , 0 \right)$ 
C) y-intercept: $\left( 0 , - \frac { 1 } { 4 } \right)$ 
D) x-intercept: $\left( \frac { 1 } { 4 } , 0 \right)$ 
E) x-intercept: $\left( - \frac { 1 } { 4 } , 0 \right)$ and y-intercept: $\left( 0 , - \frac { 1 } { 4 } \right)$

Question 18

Find all intercepts of the following function.​ $$g ( s ) = \frac { 5 s } { s ^ { 2 } + 5 }$$ ​

Accepted Answer

A) intercept: (0,0) 
B) x-intercept: (5,0) 
C) x-intercept: (-5,0) 
D) y-intercept: (0,-5) 
E) y-intercept: (0,5) 
A) intercept: (0,0) 
B) x-intercept: (5,0) 
C) x-intercept: (-5,0) 
D) y-intercept: (0,-5) 
E) y-intercept: (0,5)

Question 19

Select the correct graph of the following function. $$f ( x ) = \frac { x ^ { 2 } } { 6 x + 1 }$$ ​

Accepted Answer

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

Question 20

Select the correct graph of the function $$f ( x ) = \frac { x - 4 } { x - 7 }$$ . ​

Accepted Answer

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

Exam 16: Rational Functions

Given f(x)=x2−16x+4,g(x)=x−4f ( x ) = \frac { x ^ { 2 } - 16 } { x + 4 } , g ( x ) = x - 4f(x)=x+4x2−16​,g(x)=x−4 .Complete the table and explain how the two functions differ. x -6 -5.5 -5 -4.5 -4 -3.5 -3 f(x) g(x) ​

Determine the zeros (if any)of the rational function f(x)=x2−4x+3f ( x ) = \frac { x ^ { 2 } - 4 } { x + 3 }f(x)=x+3x2−4​ .

Find the domain of the function and identify any vertical and horizontal asymptotes.​ f(x)=2x2x+3f ( x ) = \frac { 2 x ^ { 2 } } { x + 3 }f(x)=x+32x2​ ​

Select the graph of the rational function f(x)=−x+6x+7f ( x ) = - \frac { x + 6 } { x + 7 }f(x)=−x+7x+6​ . ​

Determine the domain of f(x)=6x+6x2−6xf ( x ) = \frac { 6 x + 6 } { x ^ { 2 } - 6 x }f(x)=x2−6x6x+6​ .

Find domain of the following function. g(x)=x2−4x2−3x+2g ( x ) = \frac { x ^ { 2 } - 4 } { x ^ { 2 } - 3 x + 2 }g(x)=x2−3x+2x2−4​ ​

Determine the domain of the function f(x)=x2−9x2+4x+3f ( x ) = \frac { x ^ { 2 } - 9 } { x ^ { 2 } + 4 x + 3 }f(x)=x2+4x+3x2−9​ .

Determine the zeros (if any)of the rational function g(x)=x3−8x2+6g ( x ) = \frac { x ^ { 3 } - 8 } { x ^ { 2 } + 6 }g(x)=x2+6x3−8​ .

Find all intercepts of the following function.​ f(x)=4x2−6x+6x−4f ( x ) = \frac { 4 x ^ { 2 } - 6 x + 6 } { x - 4 }f(x)=x−44x2−6x+6​ ​

Select the correct graph of the following function.​ f(x)=x2−16x+4f ( x ) = \frac { x ^ { 2 } - 16 } { x + 4 }f(x)=x+4x2−16​ ​ ​

Simplify f(x)and find any vertical asymptotes. ​​ f(x)=x2−4x+2f ( x ) = \frac { x ^ { 2 } - 4 } { x + 2 }f(x)=x+2x2−4​ ​

Find the domain of the function and identify any vertical and horizontal asymptotes.​ f(x)=9(x−3)3f ( x ) = \frac { 9 } { ( x - 3 ) ^ { 3 } }f(x)=(x−3)39​ ​

Select the correct graph for the following rational function.​ f(x)=11x−8f ( x ) = \frac { 11 } { x - 8 }f(x)=x−811​ ​

Find the domain of the function and identify any vertical and horizontal asymptotes.​ f(x)=25x2f ( x ) = \frac { 25 } { x ^ { 2 } }f(x)=x225​ ​

Find vertical and horizontal asymptotes.​ f(x)=9+6x6+xf ( x ) = \frac { 9 + 6 x } { 6 + x }f(x)=6+x9+6x​ ​

Select the correct rational function for the following graph.​ ​

Find all intercepts of the following function.​ g(x)=1x−4g ( x ) = \frac { 1 } { x - 4 }g(x)=x−41​ ​

Find all intercepts of the following function.​ g(s)=5ss2+5g ( s ) = \frac { 5 s } { s ^ { 2 } + 5 }g(s)=s2+55s​ ​

Select the correct graph of the following function. f(x)=x26x+1f ( x ) = \frac { x ^ { 2 } } { 6 x + 1 }f(x)=6x+1x2​ ​

Select the correct graph of the function f(x)=x−4x−7f ( x ) = \frac { x - 4 } { x - 7 }f(x)=x−7x−4​ . ​

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

Given $f ( x ) = \frac { x ^ { 2 } - 16 } { x + 4 } , g ( x ) = x - 4$ .Complete the table and explain how the two functions differ. x -6 -5.5 -5 -4.5 -4 -3.5 -3 f(x) g(x)

Determine the zeros (if any)of the rational function $f ( x ) = \frac { x ^ { 2 } - 4 } { x + 3 }$ .

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

Select the graph of the rational function $f ( x ) = - \frac { x + 6 } { x + 7 }$ .

Determine the domain of $f ( x ) = \frac { 6 x + 6 } { x ^ { 2 } - 6 x }$ .

Find domain of the following function. $g ( x ) = \frac { x ^ { 2 } - 4 } { x ^ { 2 } - 3 x + 2 }$

Determine the domain of the function $f ( x ) = \frac { x ^ { 2 } - 9 } { x ^ { 2 } + 4 x + 3 }$ .

Determine the zeros (if any)of the rational function $g ( x ) = \frac { x ^ { 3 } - 8 } { x ^ { 2 } + 6 }$ .

Find all intercepts of the following function. $f ( x ) = \frac { 4 x ^ { 2 } - 6 x + 6 } { x - 4 }$

Select the correct graph of the following function. $f ( x ) = \frac { x ^ { 2 } - 16 } { x + 4 }$

Simplify f(x)and find any vertical asymptotes. $f ( x ) = \frac { x ^ { 2 } - 4 } { x + 2 }$

Find the domain of the function and identify any vertical and horizontal asymptotes. $f ( x ) = \frac { 9 } { ( x - 3 ) ^ { 3 } }$

Select the correct graph for the following rational function. $f ( x ) = \frac { 11 } { x - 8 }$

Find the domain of the function and identify any vertical and horizontal asymptotes. $f ( x ) = \frac { 25 } { x ^ { 2 } }$

Find vertical and horizontal asymptotes. $f ( x ) = \frac { 9 + 6 x } { 6 + x }$

Select the correct rational function for the following graph.

Find all intercepts of the following function. $g ( x ) = \frac { 1 } { x - 4 }$

Find all intercepts of the following function. $g ( s ) = \frac { 5 s } { s ^ { 2 } + 5 }$

Select the correct graph of the following function. $f ( x ) = \frac { x ^ { 2 } } { 6 x + 1 }$

Select the correct graph of the function $f ( x ) = \frac { x - 4 } { x - 7 }$ .