We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

College Algebra : Graphs

Study concepts, example questions & explanations for College Algebra

Create An Account

All College Algebra Resources

5 Diagnostic Tests 84 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #5 : Transformations

Give the equation of the horizontal asymptote of the graph of the equation

$f(x) =4 \log (x- 3)- 2$ .

Possible Answers:

The graph of f(x) does not have a horizontal asymptote.

y = 4

y = 3

y = 10

y = 2

Correct answer:

The graph of f(x) does not have a horizontal asymptote.

Explanation:

Let $g(x) = \log x$ . In terms of g(x) ,

f(x) =4 g (x- 3)- 2

g(x) , being a logarithmic function, has a graph without a horizontal asymptote. As f(x) represents the result of transformations of g(x) , it follows that its graph does not have a horizontal asymptote, either.

Report an Error

Example Question #61 : Graphs

Give the equation of the vertical asymptote of the graph of the equation

$f(x) =4 \log (x- 3)- 2$ .

Possible Answers:

x = 4

x = 2

x = 3

x = -3

x = -2

Correct answer:

x = 3

Explanation:

Let $g(x) = \log x$ . In terms of g(x) ,

f(x) =4 g (x- 3)- 2

The graph of g(x) has as its vertical asymptote the line of the equation x= 0 . The graph of f(x) is the result of three transformations on the graph of g(x) - a right shift of 3 units ( ), a vertical stretch ( ), and a downward shift of 2 units ( ). Of the three transformations, only the right shift affects the position of the vertical asymptote; the asymptote of f(x) also shifts right 3 units, to x = 3 .

Report an Error

Example Question #4 : Transformations

Define

$f(x) = e^{x}$

and

$g(x)= -e^{x-2}$ .

Which two transformations must be performed in the graph of f(x) in order to obtain the graph of g(x) ?

Possible Answers:

The graph of f(x) must be translated two units left, then reflected about the -axis.

The graph of f(x) must be translated two units right, then reflected about the -axis.

None of the other choices gives the correct response.

The graph of f(x) must be translated two units left, then reflected about the -axis.

Correct answer:

The graph of f(x) must be translated two units right, then reflected about the -axis.

Explanation:

g(x) = -f(x-2) , so the graph of g(x) is the result of performing the following transformations:

1) $f_{1}(x) = f(x-2)$ is the result of translating this graph two units right.

2) $g(x)= -f_{1}(x) = -f(x-2)$ is the result of reflecting the new graph about the -axis.

Report an Error

Example Question #62 : Graphs

The graph of a function f(x) is reflected about the -axis, then translated upward $\frac{8}{3}$ units. Which of the following is represented by the resulting graph?

Possible Answers:

$g(x)= -f(x) + \frac{8}{3}$

$g(x)= -f\left (x + \frac{8}{3} \right )$

$g(x)= -f\left (x- \frac{8}{3} \right )$

$g(x)= f(-x) + \frac{8}{3}$

$g(x)= -f\left (-x + \frac{8}{3} \right )$

Correct answer:

$g(x)= -f(x) + \frac{8}{3}$

Explanation:

Reflecting the graph of a function f(x) about the -axis results in the graph of the function

$f_{1}(x)= -f(x)$ .

Translating this graph upward $\frac{8}{3}$ results in the graph of the function

$g(x)= f_{1}(x) + \frac{8}{3 }= -f(x)+ \frac{8}{3 }$ .

Report an Error

Example Question #63 : Graphs

Translate the graph of $f(x) = \ln x$ upward three units to yield the graph of a function g(x) . Which of the following is a valid way of stating the definition of g(x) ?

Possible Answers:

$g(x)= \ln (x+3)$

$g(x)= \ln (e^{3} x)$

$g(x)= \ln \left ( \frac{x}{e^{3}} \right )$

$g(x)= \ln (x-3)$

$g(x)= \ln x^{3}$

Correct answer:

$g(x)= \ln (e^{3} x)$

Explanation:

A vertical translation of the graph of a function f(x) by units yields the graph of the function g(x)+k . A translation in an upward direction is a positive translation, so setting $f(x)= \ln x$ and k = 3 , the resulting graph becomes

$g(x)=( \ln x) +3$

$g(x)=3+ \ln x$

Apply properties of logarithms to rewrite this as

$g(x)= \ln e^{3} + \ln x$

$g(x)= \ln (e^{3} x)$ .

Report an Error

Example Question #61 : Graphs

Reflect the graph of $f(x) = \ln x$ about the -axis to yield the graph of a function g(x) . Which of the following is a valid way of stating the definition of g(x) ?

Possible Answers:

$g(x)= \ln (-x)$

$g(x)= \ln \frac{1}{x}$

None of the other choices gives the correct response.

$g(x) =e^{x}$

$g(x) = \frac{1}{\ln x}$

Correct answer:

$g(x)= \ln (-x)$

Explanation:

The reflection of the graph of a function f(x) about the -axis yields the graph of the function g(x) = f(-x) . Therefore, set $f(x) = \ln x$ and substitute for to yield the function

$g(x) = \ln (-x)$ .

Report an Error

Example Question #1 : Symmetry

Determine the symmetry of the following equation.

y=x^2-6x+10

Possible Answers:

Symmetry along the y-axis.

Does not have symmetry.

Symmetry along the x-axis.

Symmetry along the origin.

Symmetry along all axes.

Correct answer:

Does not have symmetry.

Explanation:

To check for symmetry, we are going to do three tests, which involve substitution. First one will be to check symmetry along the x-axis, replace -y=y .

-y=x^2-6x+10

This isn't equivilant to the first equation, so it's not symmetric along the x-axis.

Next is to substitute -x=x .

y=(-x)^2-6(-x)+10

y=x^2+6x+10

This is not the same, so it is not symmetric along the y-axis.

For the last test we will substitute -y=y , and -x=x

-y=(-x)^2-6(-x)+10

-y=x^2+6x+10

y=-x^2-6x-10

This isn't the same as the orginal equation, so it is not symmetric along the origin.

The answer is it is not symmetric along any axis.

Report an Error

Example Question #62 : Graphs

Untitled

Which of the following is true of the relation graphed above?

Possible Answers:

It is a function, but it is neither even nor odd.

It is an odd function

It is not a function

It is an even function

Correct answer:

It is an odd function

Explanation:

The relation graphed is a function, as it passes the vertical line test - no vertical line can pass through it more than once, as is demonstrated below:

Untitled

Also, it can be seen to be symmetrical about the origin. Consequently, for each in the domain, f(-c) = -f(c) - the function is odd.

Report an Error

Example Question #1 : Symmetry

Relation

Which of the following is true of the relation graphed above?

Possible Answers:

It is not a function

It is a function, but it is neither even nor odd.

It is an even function

It is an odd function

Correct answer:

It is an odd function

Explanation:

The relation graphed is a function, as it passes the vertical line test - no vertical line can pass through it more than once, as is demonstrated below:

Relation

Also, it is seen to be symmetric about the origin. Consequently, for each in the domain, f(-c) = -f(c) - the function is odd.

Report an Error

Example Question #1 : Symmetry

f(x) is an even function; f(9) = 10 .

True or false: It follows that f(10) = 9 .

Possible Answers:

True

False

Correct answer:

False

Explanation:

A function f(x) is even if and only if, for all in its domain, f(-x) = f(x) . It follows that if f(9) = 10 , then

f(-9)= f(9) = 10 .

No restriction is placed on any other value as a result of this information, so the answer is false.

Report an Error

View College Algebra Tutors

Leonard
Certified Tutor

Florida State University, Bachelor of Science, Environmental Science.

View College Algebra Tutors

Yucheng
Certified Tutor

The University of Texas at Austin, Bachelor of Science, Mechanical Engineering.

View College Algebra Tutors

Mohammad
Certified Tutor

Rutgers University-New Brunswick, Bachelor of Science, Mathematics. Rutgers University-New Brunswick, Master of Science, Stat...

All College Algebra Resources

5 Diagnostic Tests 84 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Calculus Tutors in Denver, Math Tutors in Philadelphia, SSAT Tutors in Houston, English Tutors in Boston, Statistics Tutors in New York City, SSAT Tutors in San Diego, SSAT Tutors in Atlanta, Spanish Tutors in New York City, ISEE Tutors in Seattle, Reading Tutors in Dallas Fort Worth

Popular Courses & Classes

GRE Courses & Classes in Dallas Fort Worth, SSAT Courses & Classes in Chicago, SAT Courses & Classes in Chicago, GMAT Courses & Classes in Miami, Spanish Courses & Classes in San Francisco-Bay Area, ISEE Courses & Classes in San Francisco-Bay Area, GMAT Courses & Classes in Washington DC, ACT Courses & Classes in Houston, ISEE Courses & Classes in Washington DC, GMAT Courses & Classes in Boston

Popular Test Prep

GMAT Test Prep in Miami, MCAT Test Prep in Atlanta, ISEE Test Prep in San Francisco-Bay Area, ACT Test Prep in San Francisco-Bay Area, GMAT Test Prep in Washington DC, ISEE Test Prep in Washington DC, LSAT Test Prep in Chicago, SAT Test Prep in New York City, SSAT Test Prep in New York City, GRE Test Prep in Chicago

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

College Algebra : Graphs

Study concepts, example questions & explanations for College Algebra

All College Algebra Resources

Example Questions

Example Question #5 : Transformations

Example Question #61 : Graphs

Example Question #4 : Transformations

Example Question #62 : Graphs

Example Question #63 : Graphs

Example Question #61 : Graphs

Example Question #1 : Symmetry

Example Question #62 : Graphs

Example Question #1 : Symmetry

Example Question #1 : Symmetry

All College Algebra Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: