Question 1

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 2

Select from the following which is the polynomial of degree n that has the given zero(s).  
Zero
Degree $x = 3$ $n = 3$

Accepted Answer

A)  $f ( x ) = x ^ { 3 } - 9 x ^ { 2 } + 27 x - 27$ 
B)  $f ( x ) = x ^ { 3 } + 9 x ^ { 2 } + 27 x - 27$ 
C)  $f ( x ) = x ^ { 3 } + 9 x ^ { 2 } + 27 x + 27$ 
D)  $f ( x ) = x ^ { 3 } - 9 x ^ { 2 } + 27 x + 27$ 
E)  $f ( x ) = x ^ { 3 } - 9 x ^ { 2 } - 27 x - 27$ 
A)  $f ( x ) = x ^ { 3 } - 9 x ^ { 2 } + 27 x - 27$ 
B)  $f ( x ) = x ^ { 3 } + 9 x ^ { 2 } + 27 x - 27$ 
C)  $f ( x ) = x ^ { 3 } + 9 x ^ { 2 } + 27 x + 27$ 
D)  $f ( x ) = x ^ { 3 } - 9 x ^ { 2 } + 27 x + 27$ 
E)  $f ( x ) = x ^ { 3 } - 9 x ^ { 2 } - 27 x - 27$

Question 3

Use the Remainder Theorem and synthetic division to find the function value.Verify your answer using another method.
  $f ( x ) = 4 x ^ { 3 } - 3 x + 3 , f \left( \frac { 1 } { 2 } \right)$

Accepted Answer

A) 3 
B) 4 
C) 2 
D) -1 
E) 0 
A) 3 
B) 4 
C) 2 
D) -1 
E) 0

Question 4

Given $f ( x ) = \frac { x ^ { 2 } - 4 x + 3 } { x - 7 }$ , determine the equations of any slant and vertical asymptote.

Accepted Answer

A) slant: y = x - 3; vertical: x = 3 
B) slant: y = x + 3; vertical: x = 7 
C) slant: none; vertical: none 
D) slant: y = x - 11; vertical: none 
E) slant: y = x + 10; vertical: x = -4 
A) slant: y = x - 3; vertical: x = 3 
B) slant: y = x + 3; vertical: x = 7 
C) slant: none; vertical: none 
D) slant: y = x - 11; vertical: none 
E) slant: y = x + 10; vertical: x = -4

Question 5

Find all the rational zeros of the function f(x) = 2x4 - 12x3 - 34x2 + 300x - 400.

Accepted Answer

A) x = -4, -5, 5, $- \frac { 1 } { 2 }$ 
B) x = 4, -5, 5, 2 
C) x = 2, 20, $- \frac { 5 } { 2 }$ , 2 
D) x = 2, 20, -5 
E) x = $\frac { 4 } { 5 }$ , $- \frac { 5 } { 2 }$ , 2, 5 
A) x = -4, -5, 5, $- \frac { 1 } { 2 }$ 
B) x = 4, -5, 5, 2 
C) x = 2, 20, $- \frac { 5 } { 2 }$ , 2 
D) x = 2, 20, -5 
E) x = $\frac { 4 } { 5 }$ , $- \frac { 5 } { 2 }$ , 2, 5

Question 6

Find vertical asymptotes of the following function. 
 $g ( x ) = \frac { x - 5 } { x ^ { 2 } - 25 }$

Accepted Answer

A) x = 25 
B) x = -5 
C) x = -25 
D) x = 5 
E) x = 0 
A) x = 25 
B) x = -5 
C) x = -25 
D) x = 5 
E) x = 0

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

A biology class performs an experiment comparing the quantity of food consumed by a certain kind of moth with the quantity supplied.The model for the experimental data is given by   $y = \frac { 1.572 x - 0.001 } { 6.367 x + 1 } , x > 0$  
Where x is the quantity (in milligrams) of food supplied and y is the quantity (in milligrams) of food consumed.
At what level of consumption will the moth become satiated?

Accepted Answer

A) About 0.297 mg 
B) About 0.347 mg 
C) About 0.397 mg 
D) About 0.247 mg 
E) About 0.447 mg 
A) About 0.297 mg 
B) About 0.347 mg 
C) About 0.397 mg 
D) About 0.247 mg 
E) About 0.447 mg

Question 9

Write the complex conjugate of the complex number.Then multiply the number by its complex conjugate. 
 $2 - 14 i$

Accepted Answer

A)  $2 + 14 i , 196$ 
B)   $2 - 14 i , 196$ 
C)   $2 - 14 i , 200$ 
D)   $- 2 + 14 i , 196$ 
E)   $2 + 14 i , 200$ 
A)  $2 + 14 i , 196$ 
B)   $2 - 14 i , 196$ 
C)   $2 - 14 i , 200$ 
D)   $- 2 + 14 i , 196$ 
E)   $2 + 14 i , 200$

Question 10

Solve the inequality and graph the solution on the real number line. 
 $\frac { x ^ { 2 } + x - 12 } { x } \geq 0$

Accepted Answer

A)  $[ - 4,0 ) \cap [ 3 , \infty )$   
B)  $[ 4,0 ) \cup [ 3 , \infty )$   
C)  $[ 4,0 ) \cup [ - 3 , \infty )$   
D)  $[ - 4,0 ) \cap [ - 3 , \infty )$   
E)  $[ - 4,0 ) \cup [ 3 , \infty )$   
A)  $[ - 4,0 ) \cap [ 3 , \infty )$   
B)  $[ 4,0 ) \cup [ 3 , \infty )$   
C)  $[ 4,0 ) \cup [ - 3 , \infty )$   
D)  $[ - 4,0 ) \cap [ - 3 , \infty )$   
E)  $[ - 4,0 ) \cup [ 3 , \infty )$

Question 11

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 12

Find all zeros of the function f(x) = (x - 4)(x + 4i)(x - 4i).

Accepted Answer

A) x = 4, -4i, 4i 
B) x = 4 
C) x = 4, 4i 
D) x = 4, -4, 4 
E) x = -4, -4i, 4i 
A) x = 4, -4i, 4i 
B) x = 4 
C) x = 4, 4i 
D) x = 4, -4, 4 
E) x = -4, -4i, 4i

Question 13

Find two positive real numbers whose product is a maximum and whose sum of the first number and four times the second is 160.

Accepted Answer

A)  $128,8$ 
B)  $88,18$ 
C)  $80,20$ 
D)  $96,16$ 
E)  $56,26$ 
A)  $128,8$ 
B)  $88,18$ 
C)  $80,20$ 
D)  $96,16$ 
E)  $56,26$

Question 14

A biology class performs an experiment comparing the quantity of food consumed by a certain kind of moth with the quantity supplied.The model for the experimental data is given by  
  $y = \frac { 1.573 x - 0.001 } { 6.360 x + 1 } , x > 0$  
Where x is the quantity (in milligrams) of food supplied and y is the quantity (in milligrams) of food consumed.
Select the correct graph of this model.

Accepted Answer

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

Question 15

Write the quotient in standard form.  
 $\frac { 7 - 9 i } { i }$

Accepted Answer

A)  $- 7 - 9 i$ 
B)   $- 9 - 7 i$ 
C)   $- 9 + 7 i$ 
D)   $9 - 7 i$ 
E)   $9 + 7 i$ 
A)  $- 7 - 9 i$ 
B)   $- 9 - 7 i$ 
C)   $- 9 + 7 i$ 
D)   $9 - 7 i$ 
E)   $9 + 7 i$

Question 16

Simplify the complex number and write it in standard form. 
 $3 i ^ { 2 } - 7 i ^ { 3 }$

Accepted Answer

A)   $- 7 + 3 i$ 
B)   $3 + 7 i$ 
C)   $- 3 - 7 i$ 
D)   $- 3 + 7 i$ 
E)   $3 - 7 i$ 
A)   $- 7 + 3 i$ 
B)   $3 + 7 i$ 
C)   $- 3 - 7 i$ 
D)   $- 3 + 7 i$ 
E)   $3 - 7 i$

Question 17

Determine the equations of any horizontal and vertical asymptotes of $f ( x ) = \frac { 2 x ^ { 2 } - x - 9 } { x ^ { 2 } + 3 x + 3 }$ .

Accepted Answer

A) horizontal: y = 4; vertical: x = 0 
B) horizontal: y = - 3; vertical: x = -4 
C) horizontal: y = 2; vertical: none 
D) horizontal: y = 1; vertical: x = - 3 
E) horizontal: y = -2; vertical: x = 3 and x = -4 
A) horizontal: y = 4; vertical: x = 0 
B) horizontal: y = - 3; vertical: x = -4 
C) horizontal: y = 2; vertical: none 
D) horizontal: y = 1; vertical: x = - 3 
E) horizontal: y = -2; vertical: x = 3 and x = -4

Question 18

Use long division to divide. $\left( x ^ { 4 } - 4 x ^ { 2 } - 2 \right) \div \left( x ^ { 2 } + x - 4 \right)$

Accepted Answer

A)  $x ^ { 2 } - x + 1 - \frac { 4 } { x ^ { 2 } - x + 1 }$ 
B)  $x ^ { 2 } - x + 1 + \frac { - 5 x + 2 } { x ^ { 2 } + x - 4 }$ 
C)  $x ^ { 2 } - x + 1$ 
D)  $x ^ { 2 } + x - 1$ 
E)  $x ^ { 2 } + x - 1 + \frac { - 5 x - 4 } { x ^ { 2 } + x - 4 }$ 
A)  $x ^ { 2 } - x + 1 - \frac { 4 } { x ^ { 2 } - x + 1 }$ 
B)  $x ^ { 2 } - x + 1 + \frac { - 5 x + 2 } { x ^ { 2 } + x - 4 }$ 
C)  $x ^ { 2 } - x + 1$ 
D)  $x ^ { 2 } + x - 1$ 
E)  $x ^ { 2 } + x - 1 + \frac { - 5 x - 4 } { x ^ { 2 } + x - 4 }$

Question 19

Find the domain of x in the expression. 
 $\sqrt { x ^ { 2 } - 4 }$

Accepted Answer

A)  $( - \infty , 2 ] \cap [ 2 , \infty )$ 
B)  $( - \infty , - 2 ] \cup [ 2 , \infty )$ 
C)  $( - \infty , - 2 ] \cap [ 2 , \infty )$ 
D)  $( - \infty , 2 ] \cup [ 2 , \infty )$ 
E)  $( - \infty , - 2 ) \cup [ 2 , \infty )$ 
A)  $( - \infty , 2 ] \cap [ 2 , \infty )$ 
B)  $( - \infty , - 2 ] \cup [ 2 , \infty )$ 
C)  $( - \infty , - 2 ] \cap [ 2 , \infty )$ 
D)  $( - \infty , 2 ] \cup [ 2 , \infty )$ 
E)  $( - \infty , - 2 ) \cup [ 2 , \infty )$

Question 20

Use long division to divide. 
 $\left( 4 x ^ { 3 } - 21 x ^ { 2 } - 33 x + 28 \right) \div ( 4 x + 7 )$

Accepted Answer

A)  $x ^ { 2 } - 7 x - 4 , x \neq - \frac { 7 } { 4 }$ 
B)  $4 x ^ { 3 } - 7 x + 4 , x \neq - \frac { 7 } { 4 }$ 
C)  $x ^ { 2 } + 7 x + 4 , x \neq - \frac { 7 } { 4 }$ 
D)  $x ^ { 2 } - 7 x + 4 , x \neq - \frac { 7 } { 4 }$ 
E)  $4 x ^ { 2 } - 7 x - 4 , x \neq - \frac { 7 } { 4 }$ 
A)  $x ^ { 2 } - 7 x - 4 , x \neq - \frac { 7 } { 4 }$ 
B)  $4 x ^ { 3 } - 7 x + 4 , x \neq - \frac { 7 } { 4 }$ 
C)  $x ^ { 2 } + 7 x + 4 , x \neq - \frac { 7 } { 4 }$ 
D)  $x ^ { 2 } - 7 x + 4 , x \neq - \frac { 7 } { 4 }$ 
E)  $4 x ^ { 2 } - 7 x - 4 , x \neq - \frac { 7 } { 4 }$

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

Select from the following which is the polynomial of degree n that has the given zero(s). Zero Degree $x = 3$ $n = 3$

Use the Remainder Theorem and synthetic division to find the function value.Verify your answer using another method. $f ( x ) = 4 x ^ { 3 } - 3 x + 3 , f \left( \frac { 1 } { 2 } \right)$

Given $f ( x ) = \frac { x ^ { 2 } - 4 x + 3 } { x - 7 }$ , determine the equations of any slant and vertical asymptote.

Find all the rational zeros of the function f(x) = 2x⁴ - 12x³ - 34x² + 300x - 400.

Find vertical asymptotes of the following function. $g ( x ) = \frac { x - 5 } { x ^ { 2 } - 25 }$

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

Write the complex conjugate of the complex number.Then multiply the number by its complex conjugate. $2 - 14 i$

Solve the inequality and graph the solution on the real number line. $\frac { x ^ { 2 } + x - 12 } { x } \geq 0$

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

Find all zeros of the function f(x) = (x - 4)(x + 4i)(x - 4i).

Find two positive real numbers whose product is a maximum and whose sum of the first number and four times the second is 160.

Write the quotient in standard form. $\frac { 7 - 9 i } { i }$

Simplify the complex number and write it in standard form. $3 i ^ { 2 } - 7 i ^ { 3 }$

Determine the equations of any horizontal and vertical asymptotes of $f ( x ) = \frac { 2 x ^ { 2 } - x - 9 } { x ^ { 2 } + 3 x + 3 }$ .

Use long division to divide. $\left( x ^ { 4 } - 4 x ^ { 2 } - 2 \right) \div \left( x ^ { 2 } + x - 4 \right)$

Find the domain of x in the expression. $\sqrt { x ^ { 2 } - 4 }$

Use long division to divide. $\left( 4 x ^ { 3 } - 21 x ^ { 2 } - 33 x + 28 \right) \div ( 4 x + 7 )$

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. f(x)=4x2−6x+6x−4f ( x ) = \frac { 4 x ^ { 2 } - 6 x + 6 } { x - 4 }f(x)=x−44x2−6x+6​

Select from the following which is the polynomial of degree n that has the given zero(s). Zero Degree x=3x = 3x=3 n=3n = 3n=3

Use the Remainder Theorem and synthetic division to find the function value.Verify your answer using another method. f(x)=4x3−3x+3,f(12)f ( x ) = 4 x ^ { 3 } - 3 x + 3 , f \left( \frac { 1 } { 2 } \right)f(x)=4x3−3x+3,f(21​)

Given f(x)=x2−4x+3x−7f ( x ) = \frac { x ^ { 2 } - 4 x + 3 } { x - 7 }f(x)=x−7x2−4x+3​ , determine the equations of any slant and vertical asymptote.

Find all the rational zeros of the function f(x) = 2x4 - 12x3 - 34x2 + 300x - 400.

Find vertical asymptotes of the following function. g(x)=x−5x2−25g ( x ) = \frac { x - 5 } { x ^ { 2 } - 25 }g(x)=x2−25x−5​

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​ .

Write the complex conjugate of the complex number.Then multiply the number by its complex conjugate. 2−14i2 - 14 i2−14i

Solve the inequality and graph the solution on the real number line. x2+x−12x≥0\frac { x ^ { 2 } + x - 12 } { x } \geq 0xx2+x−12​≥0

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

Find all zeros of the function f(x) = (x - 4)(x + 4i)(x - 4i).

Find two positive real numbers whose product is a maximum and whose sum of the first number and four times the second is 160.

Write the quotient in standard form. 7−9ii\frac { 7 - 9 i } { i }i7−9i​

Simplify the complex number and write it in standard form. 3i2−7i33 i ^ { 2 } - 7 i ^ { 3 }3i2−7i3

Determine the equations of any horizontal and vertical asymptotes of f(x)=2x2−x−9x2+3x+3f ( x ) = \frac { 2 x ^ { 2 } - x - 9 } { x ^ { 2 } + 3 x + 3 }f(x)=x2+3x+32x2−x−9​ .

Use long division to divide. (x4−4x2−2)÷(x2+x−4)\left( x ^ { 4 } - 4 x ^ { 2 } - 2 \right) \div \left( x ^ { 2 } + x - 4 \right)(x4−4x2−2)÷(x2+x−4)

Find the domain of x in the expression. x2−4\sqrt { x ^ { 2 } - 4 }x2−4​

Use long division to divide. (4x3−21x2−33x+28)÷(4x+7)\left( 4 x ^ { 3 } - 21 x ^ { 2 } - 33 x + 28 \right) \div ( 4 x + 7 )(4x3−21x2−33x+28)÷(4x+7)

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. $f ( x ) = \frac { 4 x ^ { 2 } - 6 x + 6 } { x - 4 }$

Select from the following which is the polynomial of degree n that has the given zero(s). Zero Degree $x = 3$ $n = 3$

Use the Remainder Theorem and synthetic division to find the function value.Verify your answer using another method. $f ( x ) = 4 x ^ { 3 } - 3 x + 3 , f \left( \frac { 1 } { 2 } \right)$

Given $f ( x ) = \frac { x ^ { 2 } - 4 x + 3 } { x - 7 }$ , determine the equations of any slant and vertical asymptote.

Find all the rational zeros of the function f(x) = 2x⁴ - 12x³ - 34x² + 300x - 400.

Find vertical asymptotes of the following function. $g ( x ) = \frac { x - 5 } { x ^ { 2 } - 25 }$

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

Write the complex conjugate of the complex number.Then multiply the number by its complex conjugate. $2 - 14 i$

Solve the inequality and graph the solution on the real number line. $\frac { x ^ { 2 } + x - 12 } { x } \geq 0$

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

Write the quotient in standard form. $\frac { 7 - 9 i } { i }$

Simplify the complex number and write it in standard form. $3 i ^ { 2 } - 7 i ^ { 3 }$

Determine the equations of any horizontal and vertical asymptotes of $f ( x ) = \frac { 2 x ^ { 2 } - x - 9 } { x ^ { 2 } + 3 x + 3 }$ .

Use long division to divide. $\left( x ^ { 4 } - 4 x ^ { 2 } - 2 \right) \div \left( x ^ { 2 } + x - 4 \right)$

Find the domain of x in the expression. $\sqrt { x ^ { 2 } - 4 }$

Use long division to divide. $\left( 4 x ^ { 3 } - 21 x ^ { 2 } - 33 x + 28 \right) \div ( 4 x + 7 )$