GMAT Math : Understanding functions

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

22 Diagnostic Tests 693 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Understanding Functions

There is water tank already $\frac{4}{7}$ full. If Jose adds 5 gallons of water to the water tank, the tank will be $\frac{13}{14}$ full. How many gallons of water would the water tank hold if it were full?

Possible Answers:

$15$

$20$

$14$

$5$

$25$

Correct answer:

$14$

Explanation:

In this case, we need to solve for the volume of the water tank, so we set the full volume of the water tank as $x$ . According to the question, $\frac{4}{7}$ -full can be replaced as $\frac{4}{7}x$ . $\frac{13}{14}$ -full would be $\frac{13}{14}x$ . Therefore, we can write out the equation as:

$\frac{4}{7}x+5=\frac{13}{14}x$ .

Then we can solve the equation and find the answer is 14 gallons.

Report an Error

Example Question #2 : Understanding Functions

There exists a set = {1, 2, 3, 4}. Which of the following defines a function of ?

Possible Answers:

two are functions

$g=\left \{ (3,1),(4,2),(1,1) \right \}$

$h=\left \{ (2,1),(3,4),(1,4),(2,1),(4,4) \right \}$

$f=\left \{ (2,3),(1,4),(2,1),(3,2),(4,4) \right \}$

none are functions

Correct answer:

$h=\left \{ (2,1),(3,4),(1,4),(2,1),(4,4) \right \}$

Explanation:

Let's look at $f,g,and\ h$ and see if any of them are functions.

1. = {(2, 3), (1, 4), (2, 1), (3, 2), (4, 4)}: This cannot be a function of because two of the ordered pairs, (2, 3) and (2, 1) have the same number (2) as the first coordinate.

2. = {(3, 1), (4, 2), (1, 1)}: This cannot be a function of because it contains no ordered pair with first coordinate 2. Because the set = {1, 2, 3, 4}, we need an ordered pair of the form (2, ) .

3. = {(2, 1), (3, 4), (1, 4), (2, 1), (4, 4)}: This is a function. Even though two of the ordered pairs have the same number (2) as the first coordinate, is still a function of because (2, 1) is simply repeated twice, so the two ordered pairs with first coordinate 2 are equal.

Report an Error

Example Question #1 : Understanding Functions

Let be a function that assigns $x^{2}$ to each real number . Which of the following is NOT an appropriate way to define ?

Possible Answers:

$y=x^{2}$

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

$f(y)=x^{2}$

all are appropriate ways to define

$x\rightarrow x^{2}$

Correct answer:

$f(y)=x^{2}$

Explanation:

This is a definition question. The only choice that does not equal the others is $f(y)=x^{2}$ . This describes a function that assigns $x^{2}$ to some number , instead of assigning $x^{2}$ to its own square root, .

Report an Error

Example Question #1 : Functions/Series

If $f(x)=x^{2}$ , find $\frac{f(x+h)-f(x)}{h}$ .

Possible Answers:

$x^{2}+4x+4$

2x+h

$x^{2}+2xh+h^{2}$

$x^{2}$

Correct answer:

2x+h

Explanation:

We are given f(x) and h, so the only missing piece is f(x + h).

$f(x+h)=(x+h)^{2}=x^{2}+2xh+h^{2}$

Then $\frac{f(x+h)-f(x)}{h}= \frac{x^{2}+2xh+h^{2}-x^{2}}{h} = \frac{2xh+h^{2}}{h}=2x+h$

Report an Error

Example Question #2 : Understanding Functions

Give the range of the function:

$f (x) = \left\{\begin{matrix} 2x - 1 & & x < -2\\ -3x& & -2\leq x\leq 2\ \\5 & & \; x > 2 \end{matrix}\right.$

Possible Answers:

$[-6, \infty )$

$(-\infty , 6]$

$(-\infty , -6] \cup [-5, 6]$

$[-5, \infty)$

$(-\infty , 5]$

Correct answer:

$(-\infty , 6]$

Explanation:

We look at the range of the function on each of the three parts of the domain. The overall range is the union of these three intervals.

On $(-\infty , -2)$ , f (x) takes the values:

x < -2

2x - 1 < 2 (-2) - 1

2x - 1 < -5

$f\left (x \right )< -5$

or $(-\infty , -5)$

On [-2, 2] , f (x) takes the values:

$-2 \leq x\leq 2$

$-3(-2) \geq -3x\geq -3 (2)$

$6 \geq -3x\geq -6$

$-6 \leq f(x)\leq 6$ ,

or [-6, 6]

On $(2, \infty)$ , f (x) takes only value 5.

The range of f (x) is therefore $(-\infty , -5) \cup [-6, 6] \cup \left \{ 5\right \}$ , which simplifies to $(-\infty , 6]$ .

Report an Error

Example Question #1 : Understanding Functions

A sequence begins as follows:

8, 12, ...

It is formed the same way that the Fibonacci sequence is formed. What are the next two numbers in the sequence?

Possible Answers:

18, 27

8, 4

20, 32

16, 20

20, 35

Correct answer:

20, 32

Explanation:

Each term of the Fibonacci sequence is formed by adding the previous two terms. Therefore, do the same to form this sequence:

8 + 12= 20

12+20=32

Report an Error

Example Question #7 : Understanding Functions

Give the inverse of f (x) = 5x - 7

Possible Answers:

$f^{-1}(x)= -\frac{1}{5}x +7$

$f^{-1}(x)= \frac{1}{5}x + \frac{7}{5}$

$f^{-1}(x)=- \frac{1}{5}x + \frac{7}{5}$

$f^{-1}(x)= \frac{1}{5}x +7$

$f^{-1}(x)= \frac{1}{5}x - \frac{7}{5}$

Correct answer:

$f^{-1}(x)= \frac{1}{5}x + \frac{7}{5}$

Explanation:

The easiest way to find the inverse of f (x) is to replace f (x) in the definition with , switch with , and solve for in the new equation.

y = 5x - 7

x = 5y - 7

x + 7 = 5y - 7 + 7

x + 7 = 5y

$\frac{1}{5} \cdot\left ( x + 7 \right ) = \frac{1}{5} \cdot 5y$

$\frac{1}{5} x + \frac{7}{5} = y$

$f^{-1}(x)= \frac{1}{5}x + \frac{7}{5}$

Report an Error

Example Question #3 : Understanding Functions

Define $f (x) = x^{3} - 8$ . Give $f^{-1} (x)$

Possible Answers:

$f^{-1}(x) = \sqrt[3]{x +2}$

$f^{-1}(x) = 8+ \sqrt[3]{x }$

$f^{-1}(x) = \sqrt[3]{x +8}$

$f^{-1}(x) = 2- \sqrt[3]{x }$

$f^{-1}(x) = 2+ \sqrt[3]{x }$

Correct answer:

$f^{-1}(x) = \sqrt[3]{x +8}$

Explanation:

The easiest way to find the inverse of f (x) is to replace f (x) in the definition with , switch with , and solve for in the new equation.

$y = x^{3} - 8$

$x= y^{3} - 8$

$x +8= y^{3} - 8 +8$

$x +8= y^{3}$

$\sqrt[3]{x +8}= \sqrt[3]{y^{3}}$

$y = \sqrt[3]{x +8}$

Report an Error

Example Question #4 : Understanding Functions

Define $f(x) = x^{2}- 4$ and $g(x) = x^{2} + 4$ .

Give the definition of $(f \circ g)(x)$ .

Possible Answers:

$(f \circ g)(x) = x^{4} - 8x^{2} +20$

$(f \circ g)(x) = x^{4}$

$(f \circ g)(x) = x^{4}+8x^{2}-12$

$(f \circ g)(x) = x^{4} -16$

$(f \circ g)(x) = x^{4}+8x^{2}+12$

Correct answer:

$(f \circ g)(x) = x^{4}+8x^{2}+12$

Explanation:

$(f \circ g)(x) = f(g(x))$

$= f(x^{2}+4)$

$= (x^{2}+4)^{2}-4$

$=x^{4} + 8x^{2}+16-4$

$=x^{4} + 8x^{2}+12$

Report an Error

Example Question #10 : Understanding Functions

Define g (x) = 5x - 2 .

If g (A) = 11 , evaluate .

Possible Answers:

A=4.2

A=53

A=57

A=2.6

A=1.8

Correct answer:

A=2.6

Explanation:

Solve for in this equation:

g (A) = 5A - 2 = 11

5A - 2 + 2 = 11+ 2

5A = 13

$5A \div 5 = 13\div 5$

A = 2.6

Report an Error

All GMAT Math Resources

22 Diagnostic Tests 693 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

GMAT Tutors in Washington DC, SSAT Tutors in San Francisco-Bay Area, Chemistry Tutors in Seattle, LSAT Tutors in San Francisco-Bay Area, SAT Tutors in Miami, LSAT Tutors in Washington DC, Math Tutors in San Diego, ISEE Tutors in Boston, SSAT Tutors in Philadelphia, Physics Tutors in New York City

Popular Courses & Classes

LSAT Courses & Classes in Miami, GMAT Courses & Classes in Chicago, SSAT Courses & Classes in Washington DC, LSAT Courses & Classes in Chicago, MCAT Courses & Classes in Houston, ISEE Courses & Classes in Denver, Spanish Courses & Classes in Boston, GRE Courses & Classes in Atlanta, Spanish Courses & Classes in Dallas Fort Worth, ACT Courses & Classes in Seattle

Popular Test Prep

SAT Test Prep in Chicago, ACT Test Prep in Miami, LSAT Test Prep in Washington DC, SAT Test Prep in Boston, LSAT Test Prep in Phoenix, SSAT Test Prep in Philadelphia, ACT Test Prep in Seattle, GMAT Test Prep in Philadelphia, MCAT Test Prep in Los Angeles, GRE Test Prep in Philadelphia

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)

Email address:
Your name:
Feedback:

GMAT Math : Understanding functions

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #1 : Understanding Functions

Example Question #2 : Understanding Functions

Example Question #1 : Understanding Functions

Example Question #1 : Functions/Series

Example Question #2 : Understanding Functions

Example Question #1 : Understanding Functions

Example Question #7 : Understanding Functions

Example Question #3 : Understanding Functions

Example Question #4 : Understanding Functions

Example Question #10 : Understanding Functions

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details