We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

SAT II Math II : Range and Domain

Study concepts, example questions & explanations for SAT II Math II

Create An Account

All SAT II Math II Resources

2 Diagnostic Tests 130 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Functions And Graphs

Define $f(x)= \frac{x- 4}{x-7}$ .

Give the range of .

Possible Answers:

$(-\infty, 7) \cup (7, \infty)$

$(-\infty, 4) \cup (4, 7) \cup (7, \infty)$

The correct range is not among the other responses.

$(-\infty, 4) \cup (7, \infty)$

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

Correct answer:

The correct range is not among the other responses.

Explanation:

The function can be rewritten as follows:

$f(x)= \frac{x- 4}{x-7}$

$f(x)= \frac{x- 7 + 3}{x-7}$

$f(x)= \frac{x- 7 }{x-7}+ \frac{ 3}{x-7}$

$f(x)=1+ \frac{ 3}{x-7}$

The expression $\frac{ 3}{x-7}$ can assume any value except for 0, so the expression $f(x)=1+ \frac{ 3}{x-7}$ can assume any value except for 1. The range is therefore the set of all real numbers except for 1, or

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

This choice is not among the responses.

Report an Error

Example Question #2 : Functions And Graphs

Define $f(x)= \frac{x- 4}{x-7}$ .

Give the domain of .

Possible Answers:

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

(4,7)

$(-\infty, 7) \cup (7, \infty)$

$(-\infty, 4) \cup (7, \infty)$

$(-\infty, 4) \cup (4, 7) \cup (7, \infty)$

Correct answer:

$(-\infty, 7) \cup (7, \infty)$

Explanation:

In a rational function, the domain excludes exactly the value(s) of the variable which make the denominator equal to 0. Set the denominator to find these values:

x- 7 =0

x = 7

The domain is the set of all real numbers except 7 - that is, $(-\infty, 7) \cup (7, \infty)$ .

Report an Error

Example Question #3 : Functions And Graphs

Define $f(x) = \sqrt[3]{100 - x^{2}}$

Give the domain of .

Possible Answers:

$\left [0, 10 \right ]$

$\left [-10, 10 \right ]$

$(-\infty, \infty)$

$\left [-10, \infty)$

$(-\infty,10]$

Correct answer:

$(-\infty, \infty)$

Explanation:

Every real number has one real cube root, so there are no restrictions on the radicand of a cube root expression. The domain is the set of all real numbers.

Report an Error

Example Question #4 : Functions And Graphs

Define $f(x) = 2- 4\cos x$

Give the range of .

Possible Answers:

[-6, -2]

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

[-2,6]

[2,6]

[-6, 2]

Correct answer:

[-2,6]

Explanation:

$-1 \leq \cos x \leq 1$ for any real value of .

Therefore,

$-4(-1) \cdot \geq -4 \cdot \cos x \geq -4 \cdot 1$

$4 \geq -4 \cos x \geq -4$

$4 + 2 \geq -4 \cos x + 2 \geq -4 + 2$

$6 \geq 2-4 \cos x \geq -2$

$-2 \leq f(x) \leq 6$

The range is [-2,6] .

Report an Error

Example Question #5 : Functions And Graphs

Define $f(x) = 2- \cos 4x$

Give the range of .

Possible Answers:

[-2,2]

$\left [ 1,2\right ]$

[-2,6]

$\left [ 1,3\right ]$

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

Correct answer:

$\left [ 1,3\right ]$

Explanation:

$-1 \leq \cos \theta \leq 1$ for any real value of $\theta$ , so

$-1 \leq \cos 4x \leq 1$

$-1 \cdot \left (-1 \right ) \geq -1 \cdot \cos 4x \geq -1 \cdot 1$

$1 \geq - \cos 4x \geq -1$

$1+ 2 \geq - \cos 4x + 2 \geq -1 + 2$

$3 \geq 2 - \cos 4x \geq 1$

$1 \leq f(x) \leq 3$ ,

making the range $\left [ 1,3\right ]$ .

Report an Error

Example Question #4 : Properties Of Functions And Graphs

Define $f (x) = \sqrt{16-x^{2}}$ .

Give the range of .

Possible Answers:

[0, 4]

[0, 16]

$(-\infty, 4]$

[-4,4]

[-16,16]

Correct answer:

[0, 4]

Explanation:

The radicand within a square root symbol must be nonnegative, so

$16 - x^{2} \geq 0$

$16 \geq x^{2}$

$x^{2} \leq 16$

This happens if and only if $-4 \leq x \leq 4$ , so the domain of is [-4,4] .

$f (x) = \sqrt{16-x^{2}}$ assumes its greatest value when $16-x^{2}$ , which is the point on [-4,4] where $x^{2}$ is least - this is at x = 0 .

$f (0) = \sqrt{16-0^{2}} = \sqrt{16} = 4$

Similarly, $f (x) = \sqrt{16-x^{2}}$ assumes its least value when $16-x^{2}$ , which is the point on [-4,4] where $x^{2}$ is greatest - this is at $x = \pm 4$ .

$f (4) = \sqrt{16-4^{2}} = \sqrt{0} = 0$

$f (-4) = \sqrt{16- \left (-4 \right )^{2}} = \sqrt{0} = 0$

Therefore, the range of is [0, 4] .

Report an Error

Example Question #6 : Functions And Graphs

Define $f(x) = \frac{5}{\sin 4x}$

Give the range of .

Possible Answers:

( -5 , 5 )

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

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

$\left (- \infty, -\frac{5}{4} \right )\cup\left ( \frac{5}{4}, \infty \right )$

$\left ( -\frac{5}{4}, \frac{5}{4} \right )$

Correct answer:

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

Explanation:

$f(x) = \frac{5}{\sin 4x}$ can be rewritten as $f (x) = 5 \csc 4x$ .

For all real values of $\theta$ ,

$\csc \theta\leq -1$ or $\csc \theta\geq 1$ .

Therefore,

$\csc 4x \leq -1$ or $\csc 4x\geq 1$ and

$5 \csc 4x \leq -5$ or $5 \csc 4x\geq 5$ .

The range of is $(- \infty, -5] \cup [5, \infty)$ .

Report an Error

Example Question #4 : Properties Of Functions And Graphs

What is the domain of the function f(x)=x^2+3?

Possible Answers:

$[-\infty ,\infty]$

$(-\infty ,\infty)$

$(-3,\infty )$

$(3,\infty)$

$[3,\infty)$

Correct answer:

$(-\infty ,\infty)$

Explanation:

The domain of a function is all the x-values that in that function. The function f(x)=x^2+3 is a upward facing parabola with a vertex as (0,3). The parabola keeps getting wider and is not bounded by any x-values so it will continue forever. Parenthesis are used because infinity is not a definable number and so it can not be included.

Report an Error

Example Question #1 : Range And Domain

What is the domain of the function? $y=\sqrt{-10x+3}$

Possible Answers:

$-\frac{3}{10}\leq x\leq \frac{3}{10}$

$x\leq \frac{3}{10}$

$\textup{All real numbers.}$

$x\leq- \frac{3}{10}$

$x\geq \frac{3}{10}$

Correct answer:

$x\leq \frac{3}{10}$

Explanation:

Notice this function resembles the parent function $y=\sqrt {x}$ . The value of must be zero or greater.

Set up an inequality to determine the domain of .

$-10x+3\geq 0$

Subtract three from both sides.

$-10x+3-3\geq 0-3$

$-10x\geq -3$

Divide by negative ten on both sides. The sign will switch.

$\frac{-10x}{-10}\geq \frac{-3}{-10}$

The domain is: $x\leq \frac{3}{10}$

Report an Error

Example Question #3 : Properties Of Functions And Graphs

What is the range of the function $f(x)=\frac{2}{x}-3$ ?

Possible Answers:

All real numbers.

All real numbers except .

Correct answer:

All real numbers except .

Explanation:

Start by considering the term $\frac{2}{x}$ . $\frac{2}{x}$ will hold for all values of , except when x=0 . Thus, $\frac{2}{x}-3$ must be defined by all values except since the equation is just shifted down by .

Report an Error

View SAT Subject Test in Mathematics Level 2 Tutors

Shakeel
Certified Tutor

View SAT Subject Test in Mathematics Level 2 Tutors

Evgenii
Certified Tutor

View SAT Subject Test in Mathematics Level 2 Tutors

Nate
Certified Tutor

University of Wisconsin-Oshkosh, non degree, Prepharmacy. University of Wisconsin-Madison, Pharmaceutical Chemist, Pharmacy.

All SAT II Math II Resources

2 Diagnostic Tests 130 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Reading Tutors in Washington DC, SAT Tutors in Atlanta, ACT Tutors in Chicago, Calculus Tutors in Philadelphia, Spanish Tutors in Atlanta, GRE Tutors in Washington DC, SSAT Tutors in Boston, Reading Tutors in Seattle, LSAT Tutors in Phoenix, Reading Tutors in San Diego

Popular Courses & Classes

LSAT Courses & Classes in Washington DC, ISEE Courses & Classes in Los Angeles, SSAT Courses & Classes in San Diego, MCAT Courses & Classes in Los Angeles, GMAT Courses & Classes in Chicago, LSAT Courses & Classes in Miami, SSAT Courses & Classes in Seattle, Spanish Courses & Classes in Miami, LSAT Courses & Classes in Seattle, GMAT Courses & Classes in Atlanta

Popular Test Prep

GRE Test Prep in New York City, SSAT Test Prep in Denver, GMAT Test Prep in Philadelphia, SAT Test Prep in Philadelphia, ACT Test Prep in San Francisco-Bay Area, ISEE Test Prep in Denver, SSAT Test Prep in Philadelphia, GRE Test Prep in Chicago, GMAT Test Prep in New York City, GRE Test Prep in Dallas Fort Worth

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

SAT II Math II : Range and Domain

Study concepts, example questions & explanations for SAT II Math II

All SAT II Math II Resources

Example Questions

Example Question #1 : Functions And Graphs

Example Question #2 : Functions And Graphs

Example Question #3 : Functions And Graphs

Example Question #4 : Functions And Graphs

Example Question #5 : Functions And Graphs

Example Question #4 : Properties Of Functions And Graphs

Example Question #6 : Functions And Graphs

Example Question #4 : Properties Of Functions And Graphs

Example Question #1 : Range And Domain

Example Question #3 : Properties Of Functions And Graphs

All SAT II Math II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: