Question 1

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 2

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

Question 3

Use the Remainder Theorem and synthetic division to find the function value.Verify your answer using another method.
  $f ( x ) = 3 x ^ { 6 } - 4 x ^ { 4 } - 8 x ^ { 2 } + 3 , f ( 4 )$

Accepted Answer

A) 11,141 
B) 11,140 
C) 11,139 
D) 11,136 
E) -11,136 
A) 11,141 
B) 11,140 
C) 11,139 
D) 11,136 
E) -11,136

Question 4

Select the graph of the function $y = ( x - 1 ) ^ { 2 }$ .Compare the graph of this function with the graph of $y = x ^ { 2 }$ .

Accepted Answer

A)    Horizontal shift 3 units to the right. 
B)    Horizontal shift 4 units to the right. 
C)    Horizontal shift 5 units to the right. 
D)    Horizontal shift 1 unit to the right. 
E)    Horizontal shift 2 units to the right. 
A)    Horizontal shift 3 units to the right. 
B)    Horizontal shift 4 units to the right. 
C)    Horizontal shift 5 units to the right. 
D)    Horizontal shift 1 unit to the right. 
E)    Horizontal shift 2 units to the right.

Question 5

Find a polynomial with real coefficients that has zeros -1, 3i, and -3i.

Accepted Answer

A) x3 + 9x2 + x + 9 
B) x3 + x2 - 9x - 9 
C) x3 + x2 + 3x + 3 
D) x3 + x2 + 9x + 9 
E) x3 - x2 + 9x - 9 
A) x3 + 9x2 + x + 9 
B) x3 + x2 - 9x - 9 
C) x3 + x2 + 3x + 3 
D) x3 + x2 + 9x + 9 
E) x3 - x2 + 9x - 9

Question 6

Find domain of the following function.
 $g ( x ) = \frac { 1 - 9 x } { 1 - x }$

Accepted Answer

A) all real numbers x 
B) all real numbers x except x = 1 
C) all real numbers x except x = -9 
D) all real numbers x except x = -1 
E) all real numbers x except x = 9 
A) all real numbers x 
B) all real numbers x except x = 1 
C) all real numbers x except x = -9 
D) all real numbers x except x = -1 
E) all real numbers x except x = 9

Question 7

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

Question 8

Find real numbers a and b such that the equation is true. 
 $( a - 4 ) + ( b + 5 ) i = 13 + 11 i$

Accepted Answer

A)   $a = 20 , b = 9$ 
B)   $a = 18 , b = 7$ 
C)   $a = 19 , b = 8$ 
D)   $a = 17 , b = 6$ 
E)   $a = 21 , b = 10$ 
A)   $a = 20 , b = 9$ 
B)   $a = 18 , b = 7$ 
C)   $a = 19 , b = 8$ 
D)   $a = 17 , b = 6$ 
E)   $a = 21 , b = 10$

Question 9

Compare the graph of $n ( x ) = 7 ( x - 3 ) ^ { 2 } + 6$ with $n ( x ) = x ^ { 2 }$ .

Accepted Answer

A)  $n ( x ) = 7 ( x - 3 ) ^ { 2 } + 6$ shifts left 3 units, shifts downward 6 units, and stretches by a factor of 7. 
B)  $n ( x ) = 7 ( x - 3 ) ^ { 2 } + 6$ shifts left 3 units, shifts upward 6 units, and stretches by a factor of 7. 
C)  $n ( x ) = 7 ( x - 3 ) ^ { 2 } + 6$ shifts right 3 units, shifts downward 6 units, and shrinks by a factor of $\frac { 1 } { 7 }$ . 
D)  $n ( x ) = 7 ( x - 3 ) ^ { 2 } + 6$ shifts right 3 units, shifts upward 6 units, and shrinks by a factor of $\frac { 1 } { 7 }$ . 
E)  $n ( x ) = 7 ( x - 3 ) ^ { 2 } + 6$ shifts right 3 units, shifts upward 6 units, and stretches by a factor of 7. 
A)  $n ( x ) = 7 ( x - 3 ) ^ { 2 } + 6$ shifts left 3 units, shifts downward 6 units, and stretches by a factor of 7. 
B)  $n ( x ) = 7 ( x - 3 ) ^ { 2 } + 6$ shifts left 3 units, shifts upward 6 units, and stretches by a factor of 7. 
C)  $n ( x ) = 7 ( x - 3 ) ^ { 2 } + 6$ shifts right 3 units, shifts downward 6 units, and shrinks by a factor of $\frac { 1 } { 7 }$ . 
D)  $n ( x ) = 7 ( x - 3 ) ^ { 2 } + 6$ shifts right 3 units, shifts upward 6 units, and shrinks by a factor of $\frac { 1 } { 7 }$ . 
E)  $n ( x ) = 7 ( x - 3 ) ^ { 2 } + 6$ shifts right 3 units, shifts upward 6 units, and stretches by a factor of 7.

Question 10

Solve the inequality and graph the solution on the real number line. 
 $\frac { x + 9 } { x + 1 } - 2 < 0$

Accepted Answer

A)  $( - \infty , - 1 ) \cup ( 7 , \infty )$   
B)  $( - \infty , - 1 ) \cap ( - 7 , \infty )$   
C)  $( - \infty , 1 ) \cap ( 7 , \infty )$   
D)  $( - \infty , - 1 ) \cup ( - 7 , \infty )$   
E)  $( - \infty , - 1 ) \cap ( 7 , \infty )$   
A)  $( - \infty , - 1 ) \cup ( 7 , \infty )$   
B)  $( - \infty , - 1 ) \cap ( - 7 , \infty )$   
C)  $( - \infty , 1 ) \cap ( 7 , \infty )$   
D)  $( - \infty , - 1 ) \cup ( - 7 , \infty )$   
E)  $( - \infty , - 1 ) \cap ( 7 , \infty )$

Question 11

Find the zeros (if any) of the rational function. 
 $f ( x ) = \frac { x ^ { 3 } - 2,744 } { x ^ { 2 } + 64 }$

Accepted Answer

A) 2,744 
B) -2,744 
C) -14 
D)  14 
E) -8 
A) 2,744 
B) -2,744 
C) -14 
D)  14 
E) -8

Question 12

Write f(x) = x4 - 2x3 - x2 - 38 x + 130 as a product of linear factors. ​

Accepted Answer

A) (x - 3 - i)(x - 3 + i)(x - 2 - 3i)(x - 2 + i) 
B) (x - 3 + i)(x - 3 - i)(x - 3 + 2i)(x - 3 - 2i) 
C) (x - 3 - i)(x - 2 + 3i)(x - 2 - 3i)(x - 2 + i) 
D) (x - 3 - i)(x - 3 + i)(x - 2 - i)(x - 2 + i) 
E) (x - 3 + i)(x - 3 - i)(x + 2 + 3i)(x + 2 - 3i) 
A) (x - 3 - i)(x - 3 + i)(x - 2 - 3i)(x - 2 + i) 
B) (x - 3 + i)(x - 3 - i)(x - 3 + 2i)(x - 3 - 2i) 
C) (x - 3 - i)(x - 2 + 3i)(x - 2 - 3i)(x - 2 + i) 
D) (x - 3 - i)(x - 3 + i)(x - 2 - i)(x - 2 + i) 
E) (x - 3 + i)(x - 3 - i)(x + 2 + 3i)(x + 2 - 3i)

Question 13

Select the correct graph of the function. 
 $f ( x ) = \frac { 1 } { 3 } x ^ { 2 } + \frac { 1 } { 3 } x - \frac { 8 } { 3 }$

Accepted Answer

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

Question 14

From the graph of the quadratic function $f ( x ) = - x ^ { 2 } + 12 x + 4$ , determine the equation of the axis of symmetry.

Accepted Answer

A)  $x = 6$ 
B)  $x = 4$ 
C)  $x = 40$ 
D)  $x = - 12$ 
E)  $x = - 32$ 
A)  $x = 6$ 
B)  $x = 4$ 
C)  $x = 40$ 
D)  $x = - 12$ 
E)  $x = - 32$

Question 15

Find all real zeros of the polynomial $f ( x ) = x ^ { 4 } + 7 x ^ { 3 } + 6 x ^ { 2 }$ and determine the multiplicity of each.

Accepted Answer

A)  $x = 0 \text {, multiplicity } 2 ; x = - 1 \text {, multiplicity } 1 ; x = - 6 \text {, multiplicity } 1$ 
B)  $x = 1 , \text { multiplicity } 2 ; x = 6 , \text { multiplicity } 2$ 
C)  $x = 0 \text {, multiplicity } 2 ; x = 1 \text {, multiplicity } 1 ; x = 6 \text {, multiplicity } 1$ 
D)  $x = - 1 , \text { multiplicity } 2 ; x = - 6 , \text { multiplicity } 2$ 
E)  $x = 0 , \text { multiplicity } 1 ; x = 1 , \text { multiplicity } 1 ; x = - 1 , \text { multiplicity } 1 ; x = 6 \text {, multiplicity } 1$ 
A)  $x = 0 \text {, multiplicity } 2 ; x = - 1 \text {, multiplicity } 1 ; x = - 6 \text {, multiplicity } 1$ 
B)  $x = 1 , \text { multiplicity } 2 ; x = 6 , \text { multiplicity } 2$ 
C)  $x = 0 \text {, multiplicity } 2 ; x = 1 \text {, multiplicity } 1 ; x = 6 \text {, multiplicity } 1$ 
D)  $x = - 1 , \text { multiplicity } 2 ; x = - 6 , \text { multiplicity } 2$ 
E)  $x = 0 , \text { multiplicity } 1 ; x = 1 , \text { multiplicity } 1 ; x = - 1 , \text { multiplicity } 1 ; x = 6 \text {, multiplicity } 1$

Question 16

Solve the inequality and write the solution set in interval notation. 
 $x ^ { 8 } ( x - 2 ) \leq 0$

Accepted Answer

A)  $( - \infty , 2 ]$ 
B)  $( - \infty , - 2 ) ]$ 
C)  $( - \infty , 2 ]$. 
D)  $( - 2,2 ]$ 
E)  $( - \infty , 2 )$ 
A)  $( - \infty , 2 ]$ 
B)  $( - \infty , - 2 ) ]$ 
C)  $( - \infty , 2 ]$. 
D)  $( - 2,2 ]$ 
E)  $( - \infty , 2 )$

Question 17

Find all the rational zeros of the function. ​
X3 - 18x2 + 108x - 216
​

Accepted Answer

A) -6 
B) 0, -1 
C) 0, 6 
D) 6 
E) ±6 
A) -6 
B) 0, -1 
C) 0, 6 
D) 6 
E) ±6

Question 18

Do the operation and express the answer in a + bi form. ​
(5 - 5i) + (8 + 3i)
​

Accepted Answer

A) 2 - 13i 
B) - 13 + 2i 
C) 13 + 2i 
D) - 13 - 2i 
E) 13 - 2i 
A) 2 - 13i 
B) - 13 + 2i 
C) 13 + 2i 
D) - 13 - 2i 
E) 13 - 2i

Question 19

The graph of the function $f ( x ) = \frac { 3 } { x - 2 }$ is shown below.Determine the vertical and horizontal asymptotes of its graph.

Accepted Answer

A) horizontal: y = 0; vertical: x = 2 
B) horizontal: y = 0; vertical: x = -2 
C) horizontal: y = -2; vertical: x = 0 
D) horizontal: y = 2; vertical: x = 0 
E) horizontal: y = -2; vertical: x = 2 
A) horizontal: y = 0; vertical: x = 2 
B) horizontal: y = 0; vertical: x = -2 
C) horizontal: y = -2; vertical: x = 0 
D) horizontal: y = 2; vertical: x = 0 
E) horizontal: y = -2; vertical: x = 2

Question 20

Find the values of b such that the function $f ( x ) = - x ^ { 2 } + b x - 75$ has the given maximum value 94.

Accepted Answer

A) ±32 
B) ±28 
C) ±26 
D) ±30 
E) ±34 
A) ±32 
B) ±28 
C) ±26 
D) ±30 
E) ±34

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

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

Use the Remainder Theorem and synthetic division to find the function value.Verify your answer using another method. $f ( x ) = 3 x ^ { 6 } - 4 x ^ { 4 } - 8 x ^ { 2 } + 3 , f ( 4 )$

Select the graph of the function $y = ( x - 1 ) ^ { 2 }$ .Compare the graph of this function with the graph of $y = x ^ { 2 }$ .

Find a polynomial with real coefficients that has zeros -1, 3i, and -3i.

Find domain of the following function. $g ( x ) = \frac { 1 - 9 x } { 1 - x }$

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

Find real numbers a and b such that the equation is true. $( a - 4 ) + ( b + 5 ) i = 13 + 11 i$

Compare the graph of $n ( x ) = 7 ( x - 3 ) ^ { 2 } + 6$ with $n ( x ) = x ^ { 2 }$ .

Solve the inequality and graph the solution on the real number line. $\frac { x + 9 } { x + 1 } - 2 < 0$

Find the zeros (if any) of the rational function. $f ( x ) = \frac { x ^ { 3 } - 2,744 } { x ^ { 2 } + 64 }$

Write f(x) = x⁴ - 2x³ - x² - 38 x + 130 as a product of linear factors.

Select the correct graph of the function. $f ( x ) = \frac { 1 } { 3 } x ^ { 2 } + \frac { 1 } { 3 } x - \frac { 8 } { 3 }$

From the graph of the quadratic function $f ( x ) = - x ^ { 2 } + 12 x + 4$ , determine the equation of the axis of symmetry.

Find all real zeros of the polynomial $f ( x ) = x ^ { 4 } + 7 x ^ { 3 } + 6 x ^ { 2 }$ and determine the multiplicity of each.

Solve the inequality and write the solution set in interval notation. $x ^ { 8 } ( x - 2 ) \leq 0$

Find all the rational zeros of the function. X³ - 18x² + 108x - 216

Do the operation and express the answer in a + bi form. (5 - 5i) + (8 + 3i)

The graph of the function $f ( x ) = \frac { 3 } { x - 2 }$ is shown below.Determine the vertical and horizontal asymptotes of its graph. $The graph of the function f ( x ) = \frac { 3 } { x - 2 } is shown below.Determine the vertical and horizontal asymptotes of its graph.$

Find the values of b such that the function $f ( x ) = - x ^ { 2 } + b x - 75$ has the given maximum value 94.

Functions and Their Graphs

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Additional Topics In Trigonometery

Systems Of Equations and Inequalities

Matrices and Determinants

Sequences Series and Probability

Topics In Analytic Geometry

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

Filters

Exam 2: Polynomial and Rational Functions

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

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

Use the Remainder Theorem and synthetic division to find the function value.Verify your answer using another method. f(x)=3x6−4x4−8x2+3,f(4)f ( x ) = 3 x ^ { 6 } - 4 x ^ { 4 } - 8 x ^ { 2 } + 3 , f ( 4 )f(x)=3x6−4x4−8x2+3,f(4)

Select the graph of the function y=(x−1)2y = ( x - 1 ) ^ { 2 }y=(x−1)2 .Compare the graph of this function with the graph of y=x2y = x ^ { 2 }y=x2 .

Find a polynomial with real coefficients that has zeros -1, 3i, and -3i.

Find domain of the following function. g(x)=1−9x1−xg ( x ) = \frac { 1 - 9 x } { 1 - x }g(x)=1−x1−9x​

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​

Find real numbers a and b such that the equation is true. (a−4)+(b+5)i=13+11i( a - 4 ) + ( b + 5 ) i = 13 + 11 i(a−4)+(b+5)i=13+11i

Compare the graph of n(x)=7(x−3)2+6n ( x ) = 7 ( x - 3 ) ^ { 2 } + 6n(x)=7(x−3)2+6 with n(x)=x2n ( x ) = x ^ { 2 }n(x)=x2 .

Solve the inequality and graph the solution on the real number line. x+9x+1−2<0\frac { x + 9 } { x + 1 } - 2 < 0x+1x+9​−2<0

Find the zeros (if any) of the rational function. f(x)=x3−2,744x2+64f ( x ) = \frac { x ^ { 3 } - 2,744 } { x ^ { 2 } + 64 }f(x)=x2+64x3−2,744​

Write f(x) = x4 - 2x3 - x2 - 38 x + 130 as a product of linear factors. ​

Select the correct graph of the function. f(x)=13x2+13x−83f ( x ) = \frac { 1 } { 3 } x ^ { 2 } + \frac { 1 } { 3 } x - \frac { 8 } { 3 }f(x)=31​x2+31​x−38​

From the graph of the quadratic function f(x)=−x2+12x+4f ( x ) = - x ^ { 2 } + 12 x + 4f(x)=−x2+12x+4 , determine the equation of the axis of symmetry.

Find all real zeros of the polynomial f(x)=x4+7x3+6x2f ( x ) = x ^ { 4 } + 7 x ^ { 3 } + 6 x ^ { 2 }f(x)=x4+7x3+6x2 and determine the multiplicity of each.

Solve the inequality and write the solution set in interval notation. x8(x−2)≤0x ^ { 8 } ( x - 2 ) \leq 0x8(x−2)≤0

Find all the rational zeros of the function. ​ X3 - 18x2 + 108x - 216 ​

Do the operation and express the answer in a + bi form. ​ (5 - 5i) + (8 + 3i) ​

The graph of the function f(x)=3x−2f ( x ) = \frac { 3 } { x - 2 }f(x)=x−23​ is shown below.Determine the vertical and horizontal asymptotes of its graph.

Find the values of b such that the function f(x)=−x2+bx−75f ( x ) = - x ^ { 2 } + b x - 75f(x)=−x2+bx−75 has the given maximum value 94.

Functions and Their Graphs

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Additional Topics In Trigonometery

Systems Of Equations and Inequalities

Matrices and Determinants

Sequences Series and Probability

Topics In Analytic Geometry

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

Filters

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

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

Use the Remainder Theorem and synthetic division to find the function value.Verify your answer using another method. $f ( x ) = 3 x ^ { 6 } - 4 x ^ { 4 } - 8 x ^ { 2 } + 3 , f ( 4 )$

Select the graph of the function $y = ( x - 1 ) ^ { 2 }$ .Compare the graph of this function with the graph of $y = x ^ { 2 }$ .

Find domain of the following function. $g ( x ) = \frac { 1 - 9 x } { 1 - x }$

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

Find real numbers a and b such that the equation is true. $( a - 4 ) + ( b + 5 ) i = 13 + 11 i$

Compare the graph of $n ( x ) = 7 ( x - 3 ) ^ { 2 } + 6$ with $n ( x ) = x ^ { 2 }$ .

Solve the inequality and graph the solution on the real number line. $\frac { x + 9 } { x + 1 } - 2 < 0$

Find the zeros (if any) of the rational function. $f ( x ) = \frac { x ^ { 3 } - 2,744 } { x ^ { 2 } + 64 }$

Write f(x) = x⁴ - 2x³ - x² - 38 x + 130 as a product of linear factors.

Select the correct graph of the function. $f ( x ) = \frac { 1 } { 3 } x ^ { 2 } + \frac { 1 } { 3 } x - \frac { 8 } { 3 }$

From the graph of the quadratic function $f ( x ) = - x ^ { 2 } + 12 x + 4$ , determine the equation of the axis of symmetry.

Find all real zeros of the polynomial $f ( x ) = x ^ { 4 } + 7 x ^ { 3 } + 6 x ^ { 2 }$ and determine the multiplicity of each.

Solve the inequality and write the solution set in interval notation. $x ^ { 8 } ( x - 2 ) \leq 0$

Find all the rational zeros of the function. X³ - 18x² + 108x - 216

Do the operation and express the answer in a + bi form. (5 - 5i) + (8 + 3i)

The graph of the function $f ( x ) = \frac { 3 } { x - 2 }$ is shown below.Determine the vertical and horizontal asymptotes of its graph. $The graph of the function f ( x ) = \frac { 3 } { x - 2 } is shown below.Determine the vertical and horizontal asymptotes of its graph.$

Find the values of b such that the function $f ( x ) = - x ^ { 2 } + b x - 75$ has the given maximum value 94.