Question 1

Given $$f ( x ) = \frac { x ^ { 2 } + 25 } { x + 5 } , g ( x ) = x - 5$$ .Determine the domains of f(x)and g(x). ​

Accepted Answer

A) Domain of f(x): all real numbers except -5 Domain of g(x): all real numbers except 5 
B) Domain of f(x): all real numbers Domain of g(x): all real numbers except 5 
C) Domain of f(x): all real numbers Domain of g(x): all real numbers 
D) Domain of f(x): all real numbers except -5 Domain of g(x): all real numbers 
E) Domain of f(x): all real numbers except 5 Domain of g(x): all real numbers 
A) Domain of f(x): all real numbers except -5 Domain of g(x): all real numbers except 5 
B) Domain of f(x): all real numbers Domain of g(x): all real numbers except 5 
C) Domain of f(x): all real numbers Domain of g(x): all real numbers 
D) Domain of f(x): all real numbers except -5 Domain of g(x): all real numbers 
E) Domain of f(x): all real numbers except 5 Domain of g(x): all real numbers

Question 2

Determine the equations of any horizontal and vertical asymptotes of $f ( x ) = \frac { x ^ { 2 } + 10 x + 24 } { x ^ { 3 } + 6 x ^ { 2 } - x - 6 }$ .

Accepted Answer

A) horizontal: y = 1;vertical: x = -6 
B) horizontal: y = 0;vertical: x = 1 and x = -6 
C) horizontal: y = 0;vertical: x = -1 and x = 1 
D) horizontal: none;vertical: none 
E) horizontal: y = 0;vertical: x = -6 and x = -4 
A) horizontal: y = 1;vertical: x = -6 
B) horizontal: y = 0;vertical: x = 1 and x = -6 
C) horizontal: y = 0;vertical: x = -1 and x = 1 
D) horizontal: none;vertical: none 
E) horizontal: y = 0;vertical: x = -6 and x = -4

Question 3

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 4

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 5

Find all intercepts of the following function.​ $$f ( t ) = \frac { 1 - 8 t } { t }$$ ​

Accepted Answer

A) t-intercept: $\left( - \frac { 1 } { 8 } , 0 \right)$ 
B) t-intercept: (0,8) 
C) t-intercept: (8,0) 
D) t-intercept: $\left( \frac { 1 } { 8 } , 0 \right)$ 
E) t-intercept: $\left( 0 , \frac { 1 } { 8 } \right)$ 
A) t-intercept: $\left( - \frac { 1 } { 8 } , 0 \right)$ 
B) t-intercept: (0,8) 
C) t-intercept: (8,0) 
D) t-intercept: $\left( \frac { 1 } { 8 } , 0 \right)$ 
E) t-intercept: $\left( 0 , \frac { 1 } { 8 } \right)$

Question 6

Find the zeros of the rational function.​ $$g ( x ) = \frac { x ^ { 2 } - 9 } { x + 3 }$$ ​

Accepted Answer

A) x = 0 
B) x = -9 
C) x = 3 
D) x = 9 
E) x = -3
​ 
A) x = 0 
B) x = -9 
C) x = 3 
D) x = 9 
E) x = -3
​

Question 7

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 8

In a pilot project,a rural township is given recycling bins for separating and storing recyclable products.The cost C (in dollars)of supplying bins to p% of the population is given by​ $C = \frac { 42,000 p } { 100 - p } , 0 \leq p < 100$ ​ Select the correct graph of the cost function.
​

Accepted Answer

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

Question 9

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 10

Determine the value that the function f approaches as the magnitude of x increases.​ $$f ( x ) = \frac { 8 x - 1 } { x ^ { 2 } + 2 }$$ ​

Accepted Answer

A) 0 
B)  $- \frac { 1 } { 2 }$ 
C) -1 
D) 8 
E)  $- \frac { 1 } { 5 }$ 
A) 0 
B)  $- \frac { 1 } { 2 }$ 
C) -1 
D) 8 
E)  $- \frac { 1 } { 5 }$

Question 11

Find the domain of the function and identify any vertical and horizontal asymptotes.​ $$f ( x ) = \frac { x - 2 } { x ^ { 2 } - 4 }$$ ​

Accepted Answer

A) The domain is all real numbers x except x = ±2.There is a vertical asymptote at x = -2,and a horizontal asymptote at y = 0. 
B) The domain is all real numbers x except x = ±2.There is a vertical asymptote at x = -2,and a horizontal asymptote at y = $\frac { 1 } { 2 }$ . 
C) The domain is all real numbers x.There is a vertical asymptote at x = -4,and a horizontal asymptote at y = 0. 
D) The domain is all real numbers x except x ​= ±4.There is a vertical asymptote at x = -4,and a horizontal asymptote at y = 0. 
E) The domain is all real numbers x except x ​= ±4.There is a vertical asymptote at x = -2,and no horizontal asymptote. 
A) The domain is all real numbers x except x = ±2.There is a vertical asymptote at x = -2,and a horizontal asymptote at y = 0. 
B) The domain is all real numbers x except x = ±2.There is a vertical asymptote at x = -2,and a horizontal asymptote at y = $\frac { 1 } { 2 }$ . 
C) The domain is all real numbers x.There is a vertical asymptote at x = -4,and a horizontal asymptote at y = 0. 
D) The domain is all real numbers x except x ​= ±4.There is a vertical asymptote at x = -4,and a horizontal asymptote at y = 0. 
E) The domain is all real numbers x except x ​= ±4.There is a vertical asymptote at x = -2,and no horizontal asymptote.

Question 12

Identify all intercepts of $f ( x ) = \frac { x ^ { 2 } + 7 x + 10 } { x ^ { 3 } + 5 x ^ { 2 } - x - 5 }$ .

Accepted Answer

A) x-intercept: none;y-intercept: none 
B) x-intercept: $\left( - \frac { 7 } { 5 } , 0 \right)$ ;y-intercept: none 
C) x-intercept: (-2,0);y-intercept: (0,-2) 
D) x-intercepts: (-5,0), (-1,0), (1,0);y-intercept: (0,-2) 
E) x-intercept: (0,0);y-intercept: (0,0) 
A) x-intercept: none;y-intercept: none 
B) x-intercept: $\left( - \frac { 7 } { 5 } , 0 \right)$ ;y-intercept: none 
C) x-intercept: (-2,0);y-intercept: (0,-2) 
D) x-intercepts: (-5,0), (-1,0), (1,0);y-intercept: (0,-2) 
E) x-intercept: (0,0);y-intercept: (0,0)

Question 13

Find all intercepts of the following function.​ $$g ( x ) = \frac { - 1 } { x + 3 }$$ ​

Accepted Answer

A) x-intercept: $$\left( - \frac { 1 } { 3 } , 0 \right)$$ 
B) y-intercept: $\left( 0 , - \frac { 1 } { 3 } \right)$ 
C) x-intercept: $\left( - \frac { 1 } { 3 } , 0 \right)$ and y-intercept: $\left( 0 , - \frac { 1 } { 3 } \right)$ 
D) x-intercept: $\left( \frac { 1 } { 3 } , 0 \right)$ 
E) y-intercept: $\left( 0 , \frac { 1 } { 3 } \right)$ 
A) x-intercept: $$\left( - \frac { 1 } { 3 } , 0 \right)$$ 
B) y-intercept: $\left( 0 , - \frac { 1 } { 3 } \right)$ 
C) x-intercept: $\left( - \frac { 1 } { 3 } , 0 \right)$ and y-intercept: $\left( 0 , - \frac { 1 } { 3 } \right)$ 
D) x-intercept: $\left( \frac { 1 } { 3 } , 0 \right)$ 
E) y-intercept: $\left( 0 , \frac { 1 } { 3 } \right)$

Question 14

The cost C (in millions of dollars)of removing p% of the industrial and municipal pollutants discharged into a river is given by​ $C = \frac { 255 p } { 100 - p } , 0 \leq p \leq 100$ . ​
Select the correct graph of the cost function.
​

Accepted Answer

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

Question 15

Determine the domain of $$f ( x ) = \frac { x ^ { 2 } + 11 x + 30 } { x ^ { 3 } + 6 x ^ { 2 } - x - 6 }$$ .

Accepted Answer

A) all real numbers except x = -6 and x = -5 
B) all real numbers except x = -1,x = 1,x = -6 and x = -5 
C) all real numbers except x = 6 
D) all real numbers except x = -1,x = 1 and x = -6 
E) all real numbers 
A) all real numbers except x = -6 and x = -5 
B) all real numbers except x = -1,x = 1,x = -6 and x = -5 
C) all real numbers except x = 6 
D) all real numbers except x = -1,x = 1 and x = -6 
E) all real numbers

Question 16

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

Accepted Answer

A) horizontal: y = 0 ;vertical: x = 4 
B) horizontal: y = -4 ;vertical: x = 0 
C) horizontal: x = 0;vertical: y = 4 
D) horizontal: x = 4 ;vertical: y = -1 
E) horizontal: y = 1 ;vertical: x = 4 
A) horizontal: y = 0 ;vertical: x = 4 
B) horizontal: y = -4 ;vertical: x = 0 
C) horizontal: x = 0;vertical: y = 4 
D) horizontal: x = 4 ;vertical: y = -1 
E) horizontal: y = 1 ;vertical: x = 4

Question 17

Find the zeros (if any)of the rational function.​ $$f ( x ) = 1 - \frac { 8 } { x - 8 }$$ ​

Accepted Answer

A) ​8 
B) -1 
C) ​-16 
D) 1 
E) ​16 
A) ​8 
B) -1 
C) ​-16 
D) 1 
E) ​16

Question 18

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

Accepted Answer

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

Question 19

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

Accepted Answer

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

Question 20

Determine the domain of the function $$f ( x ) = \frac { x ^ { 2 } - 25 } { x ^ { 2 } + x - 20 }$$ .

Accepted Answer

A) Domain: all real numbers except x = 5 and -4 
B) Domain: all real numbers except x = -5 and -4 
C) Domain: all real numbers except x = -5 and 4 
D) Domain: all real numbers except x = -4 
E) Domain: all real numbers 
A) Domain: all real numbers except x = 5 and -4 
B) Domain: all real numbers except x = -5 and -4 
C) Domain: all real numbers except x = -5 and 4 
D) Domain: all real numbers except x = -4 
E) Domain: all real numbers

Exam 16: Rational Functions

Given f(x)=x2+25x+5,g(x)=x−5f ( x ) = \frac { x ^ { 2 } + 25 } { x + 5 } , g ( x ) = x - 5f(x)=x+5x2+25​,g(x)=x−5 .Determine the domains of f(x)and g(x). ​

Determine the equations of any horizontal and vertical asymptotes of f(x)=x2+10x+24x3+6x2−x−6f ( x ) = \frac { x ^ { 2 } + 10 x + 24 } { x ^ { 3 } + 6 x ^ { 2 } - x - 6 }f(x)=x3+6x2−x−6x2+10x+24​ .

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

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​ ​

Find all intercepts of the following function.​ f(t)=1−8ttf ( t ) = \frac { 1 - 8 t } { t }f(t)=t1−8t​ ​

Find the zeros of the rational function.​ g(x)=x2−9x+3g ( x ) = \frac { x ^ { 2 } - 9 } { x + 3 }g(x)=x+3x2−9​ ​

Determine the value that the function f approaches as the magnitude of x increases.​ f(x)=8x−1x2+2f ( x ) = \frac { 8 x - 1 } { x ^ { 2 } + 2 }f(x)=x2+28x−1​ ​

Find the domain of the function and identify any vertical and horizontal asymptotes.​ f(x)=x−2x2−4f ( x ) = \frac { x - 2 } { x ^ { 2 } - 4 }f(x)=x2−4x−2​ ​

Identify all intercepts of f(x)=x2+7x+10x3+5x2−x−5f ( x ) = \frac { x ^ { 2 } + 7 x + 10 } { x ^ { 3 } + 5 x ^ { 2 } - x - 5 }f(x)=x3+5x2−x−5x2+7x+10​ .

Find all intercepts of the following function.​ g(x)=−1x+3g ( x ) = \frac { - 1 } { x + 3 }g(x)=x+3−1​ ​

The cost C (in millions of dollars)of removing p% of the industrial and municipal pollutants discharged into a river is given by​ C=255p100−p,0≤p≤100C = \frac { 255 p } { 100 - p } , 0 \leq p \leq 100C=100−p255p​,0≤p≤100 . ​ Select the correct graph of the cost function. ​

Determine the domain of f(x)=x2+11x+30x3+6x2−x−6f ( x ) = \frac { x ^ { 2 } + 11 x + 30 } { x ^ { 3 } + 6 x ^ { 2 } - x - 6 }f(x)=x3+6x2−x−6x2+11x+30​ .

Determine the equations of the vertical and horizontal asymptotes of the graph of the function f(x)=xx−4f ( x ) = \frac { x } { x - 4 }f(x)=x−4x​ .

Find the zeros (if any)of the rational function.​ f(x)=1−8x−8f ( x ) = 1 - \frac { 8 } { x - 8 }f(x)=1−x−88​ ​

Select the correct graph of the following function. f(x)=−1(x−3)2f ( x ) = - \frac { 1 } { ( x - 3 ) ^ { 2 } }f(x)=−(x−3)21​ ​

Select the correct graph of the function f(x)=8x−2f ( x ) = \frac { 8 } { x - 2 }f(x)=x−28​ . ​

Determine the domain of the function f(x)=x2−25x2+x−20f ( x ) = \frac { x ^ { 2 } - 25 } { x ^ { 2 } + x - 20 }f(x)=x2+x−20x2−25​ .

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

Rotation of Conics

Given $f ( x ) = \frac { x ^ { 2 } + 25 } { x + 5 } , g ( x ) = x - 5$ .Determine the domains of f(x)and g(x).

Determine the equations of any horizontal and vertical asymptotes of $f ( x ) = \frac { x ^ { 2 } + 10 x + 24 } { x ^ { 3 } + 6 x ^ { 2 } - x - 6 }$ .

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

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

Find all intercepts of the following function. $f ( t ) = \frac { 1 - 8 t } { t }$

Find the zeros of the rational function. $g ( x ) = \frac { x ^ { 2 } - 9 } { x + 3 }$

Determine the value that the function f approaches as the magnitude of x increases. $f ( x ) = \frac { 8 x - 1 } { x ^ { 2 } + 2 }$

Find the domain of the function and identify any vertical and horizontal asymptotes. $f ( x ) = \frac { x - 2 } { x ^ { 2 } - 4 }$

Identify all intercepts of $f ( x ) = \frac { x ^ { 2 } + 7 x + 10 } { x ^ { 3 } + 5 x ^ { 2 } - x - 5 }$ .

Find all intercepts of the following function. $g ( x ) = \frac { - 1 } { x + 3 }$

The cost C (in millions of dollars)of removing p% of the industrial and municipal pollutants discharged into a river is given by $C = \frac { 255 p } { 100 - p } , 0 \leq p \leq 100$ . Select the correct graph of the cost function.

Determine the domain of $f ( x ) = \frac { x ^ { 2 } + 11 x + 30 } { x ^ { 3 } + 6 x ^ { 2 } - x - 6 }$ .

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

Find the zeros (if any)of the rational function. $f ( x ) = 1 - \frac { 8 } { x - 8 }$

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

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

Determine the domain of the function $f ( x ) = \frac { x ^ { 2 } - 25 } { x ^ { 2 } + x - 20 }$ .