Call Now to Set Up Tutoring:

(888) 888-0446

High School Math : Functions and Graphs

Study concepts, example questions & explanations for High School Math

Create An Account

All High School Math Resources

8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #11 : Functions And Graphs

If $f(x)=3x^{2}+5$ and g(x)= x-2 , what is g(f(x)) ?

Possible Answers:

$2x^{2}+5$

$3x^{2}+3$

$3x^{2}+12x-7$

$3x^{2}-12x+17$

$x^{2}-2$

Correct answer:

$3x^{2}+3$

Explanation:

g(f(x)) means f(x) gets plugged into g(x) .

Thus $g(f(x))= (3x^{2}+5) - 2 = 3x^{2}+3$ .

Report an Error

Example Question #1 : Understanding Functional Notations

Let $f(x)= x^{3}-2x^{2}+x$ and $g(x)=x^{2}-1$ . What is f(g(2)) ?

Possible Answers:

Correct answer:

Explanation:

Calculate g(2) and plug it into f(x) .

$g(2)= (2)^{2}-1=4-1=3$

$f(3)=(3)^{3}-2(3)^{2}+(3)=27-2(9)+(3)=27-18+3=12$

Report an Error

Example Question #11 : Introduction To Functions

Evaluate $\small f(g(3))$ if f(x)=6x-4 and g(x)=x^2 .

Possible Answers:

Undefined

196

Correct answer:

Explanation:

$\small f(g(3))$

This expression is the same as saying "take the answer of $\small g(3)$ and plug it into $\small f(x)$ ."

First, we need to find $\small g(3)$ . We do this by plugging $\small 3$ in for $\small x$ in $\small g(x)$ .

g(x)=x^2

g(3)=3^2=9

Now we take this answer and plug it into $\small f(x)$ .

f(g(3))=f(9)

We can find the value of $\small f(9)$ by replacing $\small x$ with $\small 9$ .

f(x)=6x-4

f(9)=6(9)-4=50

This is our final answer.

Report an Error

Example Question #1 : Transformations Of Parabolic Functions

If the function f(x) is depicted here, which answer choice graphs f(x+2) ?

Possible Answers:

None of these graphs are correct.

Correct answer:

Explanation:

The function f(x+b) shifts a function f(x) units to the left. Conversely, f(x-b) shifts a function f(x) units to the right. In this question, we are translating the graph two units to the left.

To translate along the y-axis, we use the function f(x)+k or f(x)-k .

Report an Error

Example Question #1 : Understanding Inverse Functions

Let f(x)=5-(1+x)^3 . What is $f^{-1}(x)$ ?

Possible Answers:

$f^{-1}(x)=(5-x)^{\frac{1}{3}}-1$

$f^{-1}(x)=\left (1-x)\right ^{1/3}+5$

$f^{-1}(x)=(5-x)^{3}-1$

$f^{-1}(x)=\left ((5-x)^{3}-1 )\right ^{1/3}$

$f^{-1}(x)=\left (1-5x)\right ^{1/3}+1$

Correct answer:

$f^{-1}(x)=(5-x)^{\frac{1}{3}}-1$

Explanation:

We are asked to find $f^{^{-1}} (x)$ , which is the inverse of a function.

In order to find the inverse, the first thing we want to do is replace f(x) with y. (This usually makes it easier to separate x from its function.).

y=5-(1+x)^3

Next, we will swap x and y.

x=5-(1+y)^3

Then, we will solve for y. The expression that we determine will be equal to $f^{^{-1}} (x)$ .

x=5-(1+y)^3

Subtract 5 from both sides.

x-5=-(1+y)^3

Multiply both sides by -1.

-1(x-5)=5-x=(1+y)^3

We need to raise both sides of the equation to the 1/3 power in order to remove the exponent on the right side.

$(5-x)^{\frac{1}{3}}=\left ((1+y)^{3} \right )^{1/3}$

We will apply the general property of exponents which states that $(a^b)^{c}=a^{b\cdot c}$ .

$(5-x)^{\frac{1}{3}}=\left ((1+y)^{3} \right )^{1/3}=(1+y)^{3\cdot \frac{1}{3}}=(1+y)^1=1+y$

Laslty, we will subtract one from both sides.

$(5-x)^{\frac{1}{3}}-1=y$

The expression equal to y is equal to the inverse of the original function f(x). Thus, we can replace y with $f^{-1}(x)$ .

$f^{-1}(x)=(5-x)^{\frac{1}{3}}-1$

The answer is $f^{-1}(x)=(5-x)^{\frac{1}{3}}-1$ .

Report an Error

Example Question #1 : Understanding Inverse Functions

What is the inverse of $y=4x^{2}$ ?

Possible Answers:

$y=\pm \sqrt{x}$

$y=\frac{\pm \sqrt{x}}{2}$

$y=\frac{\pm \sqrt{x}}{4}$

$y=-4x^{2}$

$y=\frac{x^{2}}{4}$

Correct answer:

$y=\frac{\pm \sqrt{x}}{2}$

Explanation:

The inverse of requires us to interchange and and then solve for .

$y=4x^{2}$

$x=4y^{2}$

Then solve for :

$y=\frac{\pm \sqrt{x}}{2}$

Report an Error

Example Question #2 : Understanding Inverse Functions

If $f(x)=x^{2}+1$ , what is $f^{-1}(x)$ ?

Possible Answers:

$f^{-1}(x)=\frac{1}{x^{2}-1}$

$f^{-1}(x)=x^{2}-1$

$f^{-1}(x)=\sqrt{x-1}$

$f^{-1}(x)=\sqrt{x^{2}+1}$

$f^{-1}(x)=\frac{1}{x^{2}+1}$

Correct answer:

$f^{-1}(x)=\sqrt{x-1}$

Explanation:

To find the inverse of a function, exchange the and variables and then solve for .

$x=y^{2}+1$

$x-1=y^{2}$

$\sqrt{x-1}=y=f^{-1}(x)$

Report an Error

Example Question #1 : Understanding Vertical And Horizontal Lines

Which of the following is a horizontal line?

Possible Answers:

y=2x+1

x = 4

y = 3x + 4

y = 0

y = -x

Correct answer:

y = 0

Explanation:

A horizontal line has infinitely many values for , but only one possible value for . Thus, it is always of the form y = c , where is a constant. Horizontal lines have a slope of . The only equation of this form is y = 0 .

Report an Error

Example Question #2 : Understanding Vertical And Horizontal Lines

Which of the following is a vertical line?

Possible Answers:

y = 3x + 2

$y = \frac{1}{x}$

y = x

y = 4

x = 3

Correct answer:

x = 3

Explanation:

A vertical line is one in which the values can vary. Namely, there is only one possible value for , and can be any number. Thus, by this description, the only vertical line listed is x = 3 .

Report an Error

Example Question #2 : Understanding Vertical And Horizontal Lines

Which of the following has a slope of 0?

Possible Answers:

$y = 3^{x}$

x = 0

y = x

y = 10

$y = \frac{1}{x}$

Correct answer:

y = 10

Explanation:

A line with a slope of zero will be horizontal. A horizontal line has only one possible value for , and can be any value.

Thus, the only given equation which fits this description is y = 10 .

Report an Error

View Tutors

Anthony
Certified Tutor

CUNY New York City College of Technology, Bachelor of Science, Civil Engineering.

View Tutors

Chiquita
Certified Tutor

Troy University, Bachelor of Science, Education. University of Phoenix-Atlanta Campus, Master of Arts, Adult and Continuing E...

View Tutors

Tracy
Certified Tutor

Clarion University of Pennsylvania, Bachelor of Science, Physics.

All High School Math Resources

8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

English Tutors in New York City, Computer Science Tutors in San Diego, Computer Science Tutors in New York City, MCAT Tutors in Philadelphia, SSAT Tutors in Atlanta, Algebra Tutors in San Diego, Calculus Tutors in San Francisco-Bay Area, SAT Tutors in Houston, ISEE Tutors in Miami, English Tutors in Los Angeles

Popular Courses & Classes

Spanish Courses & Classes in Seattle, ACT Courses & Classes in New York City, MCAT Courses & Classes in Miami, MCAT Courses & Classes in New York City, MCAT Courses & Classes in Los Angeles, SSAT Courses & Classes in San Diego, GMAT Courses & Classes in Dallas Fort Worth, Spanish Courses & Classes in Miami, LSAT Courses & Classes in Los Angeles, ACT Courses & Classes in Houston

Popular Test Prep

GRE Test Prep in Washington DC, SSAT Test Prep in Chicago, MCAT Test Prep in Los Angeles, MCAT Test Prep in Phoenix, GMAT Test Prep in Atlanta, ISEE Test Prep in Dallas Fort Worth, GRE Test Prep in New York City, MCAT Test Prep in Philadelphia, ACT Test Prep in Chicago, SAT Test Prep in San Diego

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

High School Math : Functions and Graphs

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #11 : Functions And Graphs

Example Question #1 : Understanding Functional Notations

Example Question #11 : Introduction To Functions

Example Question #1 : Transformations Of Parabolic Functions

Example Question #1 : Understanding Inverse Functions

Example Question #1 : Understanding Inverse Functions

Example Question #2 : Understanding Inverse Functions

Example Question #1 : Understanding Vertical And Horizontal Lines

Example Question #2 : Understanding Vertical And Horizontal Lines

Example Question #2 : Understanding Vertical And Horizontal Lines

All High School Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: