GMAT Math : Coordinate Geometry

Study concepts, example questions & explanations for GMAT Math

Create An Account

All GMAT Math Resources

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

Example Questions

Example Question #2 : Graphing A Point

The point (7,a) lies on a line with a slope m=4 that passes through (1,3) . What is the value of ?

Possible Answers:

Correct answer:

Explanation:

In order to find the value of , we first need to find the equation for the line with a slope m=4 that passes through (1,3) .

y-3=4(x-1)

y-3=4x-4

y=4x-1

Plugging in (7,a) and solving for :

a=4(7)-1

a=28-1

a=27

Report an Error

Example Question #1 : Graphing A Function

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

Possible Answers:

$x \leq 4$

all real numbers

$x \leq 0$

$x \geq 4$

x=0

Correct answer:

all real numbers

Explanation:

The domain of the function specifies the values that can take. Here, $4-x^{2}$ is defined for every value of , so the domain is all real numbers.

Report an Error

Example Question #2 : Graphing A Function

What is the domain of $y=-2\sqrt{x}$ ?

Possible Answers:

x>0

x<-2

x=0

$x\geq 0$

$x\leq 0$

Correct answer:

$x\geq 0$

Explanation:

To find the domain, we need to decide which values can take. The is under a square root sign, so cannot be negative. can, however, be 0, because we can take the square root of zero. Therefore the domain is $x\geq 0$ .

Report an Error

Example Question #3 : Graphing A Function

What is the domain of the function $y=\sqrt{4-x^{2}}$ ?

Possible Answers:

x<-2

x>-2

$\left ( -2,2 \right )$

$\left [ -2,2 \right ]$

$x\leq -2$

Correct answer:

$\left [ -2,2 \right ]$

Explanation:

To find the domain, we must find the interval on which $\sqrt{4-x^{2}}$ is defined. We know that the expression under the radical must be positive or 0, so $\sqrt{4-x^{2}}$ is defined when $x^{2}\leq 4$ . This occurs when $x \geq -2$ and $x \leq 2$ . In interval notation, the domain is $\left [ -2,2 \right ]$ .

Report an Error

Example Question #3 : Graphing A Function

Define the functions and as follows:

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

$\small g (x) = 6x - \sqrt{x-1}$

What is the domain of the function (f+g)(x) ?

Possible Answers:

$\small \small [1, \infty )$

$\small \small (-\infty , -1] \cup [1, \infty )$

$\small (-\infty , 1) \cup (1, \infty )$

$\small (1, \infty )$

$\small (-\infty ,\infty )$

Correct answer:

$\small \small [1, \infty )$

Explanation:

The domain of (f+g) is the intersection of the domains of and . and are each restricted to all values of that allow the radicand x-1 to be nonnegative - that is,

$\small \small x - 1\geq 0$ , or

$\small \small \small x \geq 1$

Since the domains of and are the same, the domain of (f+g) is also the same. In interval form the domain of (f+g) is $\small \small [1, \infty )$

Report an Error

Example Question #4 : How To Graph A Function

Define $g (x) = \frac{1}{\sqrt[3]{x -27}}$

What is the natural domain of ?

Possible Answers:

$(-\infty , - 27)\cup (27, \infty )$

$(-\infty , - 3)\cup (3, \infty )$

$(-\infty , 27)\cup (27, \infty )$

$(3, \infty )$

$(27, \infty )$

Correct answer:

$(-\infty , 27)\cup (27, \infty )$

Explanation:

The radical in and of itself does not restrict the domain, since every real number has a real cube root. However, since the expression $\sqrt[3]{x -27}$ is in a denominator, it cannot be equal to zero, so the domain excludes the value(s) for which

$\sqrt[3]{x -27} = 0$

$\left (\sqrt[3]{x -27} \right )^{3}= 0^{3}$

x -27 = 0

x = 27

27 is the only number excluded from the domain.

Report an Error

Example Question #5 : Graphing A Function

Define $g(x) = \frac{x}{x^{2}+3x-4 }$

What is the natural domain of ?

Possible Answers:

$( - \infty ,-1 ) \cup (-1,4) \cup (4, \infty )$

$( - \infty ,-1 ) \cup (-1,0) \cup (0,4) \cup (4, \infty )$

$( - \infty ,-4 ) \cup (-4,0) \cup (0,1) \cup (1, \infty )$

$( - \infty ,-4 ) \cup (-4,1) \cup (1, \infty )$

$( - \infty ,0) \cup (0, \infty )$

Correct answer:

$( - \infty ,-4 ) \cup (-4,1) \cup (1, \infty )$

Explanation:

Since the expression $x^{2}+3x-4$ is in a denominator, it cannot be equal to zero, so the domain excludes the value(s) for which $x^{2}+3x-4 =0$ . We solve for by factoring the polynomial, which we can do as follows:

$x^{2}+3x-4 =0$

(x+?)(x+?)=0

Replacing the question marks with integers whose product is and whose sum is 3:

(x+4)(x-1)=0

$x + 4 = 0 \Rightarrow x = -4$

$x -1 = 0 \Rightarrow x = 1$

Therefore, the domain excludes these two values of .

Report an Error

Example Question #217 : Advanced Geometry

Define $f (x) = \frac{1}{x ^{2}- 25 }$ .

What is the natural domain of ?

Possible Answers:

$(-\infty , 5 ) \cup \left ( 5, \infty)$

$(-\infty , -5 ) \cup (5, \infty)$

$(-\infty , -5 ) \cup \left ( -5, \infty)$

(-5 , 5)

$(-\infty , -5 ) \cup \left ( -5,5\right ) \cup (5, \infty)$

Correct answer:

$(-\infty , -5 ) \cup \left ( -5,5\right ) \cup (5, \infty)$

Explanation:

The only restriction on the domain of is that the denominator cannot be 0. We set the denominator to 0 and solve for to find the excluded values:

$x ^{2}-25 =0$

$x ^{2}= 25$

$x = -5 \textrm{ or }x = 5$

The domain is the set of all real numbers except those two - that is,

$(-\infty , -5 ) \cup \left ( -5,5\right ) \cup (5, \infty)$ .

Report an Error

Example Question #1 : Coordinate Geometry

What is the -intercept of the graph of $y = \log _{2}(x+ 4)$ ?

Possible Answers:

(1,0)

(-3,0)

The graph has no -intercept.

(2,0)

(-4,0)

Correct answer:

(-3,0)

Explanation:

Set y = 0 and solve:

$y = \log _{2}(x+ 4)$

$\log _{2}(x+ 4) = 0$

$2 ^ {\log _{2}(x+ 4) }= 2 ^ { 0}$

x + 4 = 1

x + 4 - 4 = 1 - 4

x = -3

The -intercept is (-3,0) .

Report an Error

Example Question #2 : Coordinate Geometry

What is the -intercept of the graph of $y = \log _{3}(x+ 9)$ ?

Possible Answers:

(0,-6)

(0,3)

The graph has no -intercept.

(0,-9)

(0,2)

Correct answer:

(0,2)

Explanation:

Set x= 0 and evaluate :

$y = \log _{3}(x+ 9)$

$y = \log _{3}(0+ 9) = \log _{3}9$

Since $3 ^{2} =9$ ,

$\log _{3}9 =2$ , and the -intercept is (0,2) .

Report an Error

All GMAT Math Resources

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

Popular Subjects

GRE Tutors in Philadelphia, ISEE Tutors in Boston, SSAT Tutors in Washington DC, MCAT Tutors in Houston, Statistics Tutors in Denver, Chemistry Tutors in Miami, ISEE Tutors in Phoenix, SSAT Tutors in New York City, Statistics Tutors in Miami, ACT Tutors in Miami

Popular Courses & Classes

Spanish Courses & Classes in Los Angeles, MCAT Courses & Classes in Phoenix, ACT Courses & Classes in Chicago, SSAT Courses & Classes in Boston, LSAT Courses & Classes in Chicago, SAT Courses & Classes in San Francisco-Bay Area, Spanish Courses & Classes in San Francisco-Bay Area, GRE Courses & Classes in Phoenix, GMAT Courses & Classes in Denver, LSAT Courses & Classes in Denver

Popular Test Prep

ISEE Test Prep in Los Angeles, MCAT Test Prep in Seattle, MCAT Test Prep in Boston, ACT Test Prep in Miami, SAT Test Prep in Miami, ACT Test Prep in Chicago, SAT Test Prep in Los Angeles, GRE Test Prep in Los Angeles, LSAT Test Prep in Houston, GMAT 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 : Coordinate Geometry

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #2 : Graphing A Point

Example Question #1 : Graphing A Function

Example Question #2 : Graphing A Function

Example Question #3 : Graphing A Function

Example Question #3 : Graphing A Function

Example Question #4 : How To Graph A Function

Example Question #5 : Graphing A Function

Example Question #217 : Advanced Geometry

Example Question #1 : Coordinate Geometry

Example Question #2 : Coordinate Geometry

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details