Call Now to Set Up Tutoring:

(888) 888-0446

Precalculus : Pre-Calculus

Study concepts, example questions & explanations for Precalculus

Create An Account

All Precalculus Resources

12 Diagnostic Tests 380 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #54 : Functions

Find the domain and range of the function.

$y=\sqrt{x}$

Possible Answers:

Domain: x>0

Range: All real numbers

Domain: All real numbers

Range: y>0

Domain: $x\ge0$

Range: $y\ge0$

Domain: All real numbers

Range: All real numbers

Correct answer:

Domain: $x\ge0$

Range: $y\ge0$

Explanation:

The domain is the set of x-values for which the function is defined.

The range is the set of y-values for which the function is defined.

Because the values for x are never negative,

and the values for y are never negative,

Domain: $x\ge0$

Range: $y\ge0$

Report an Error

Example Question #44 : Relations And Functions

What is the domain of $y=\sqrt{x-6}$

Possible Answers:

$[6,\infty)$

$(-6,\infty )$

$[-6,\infty )$

$(-\infty, \infty )$

$(6.\infty )$

Correct answer:

$[6,\infty)$

Explanation:

As long as the number under the square root sign is greater than or equal to , then the corresponding x-value is in the domain. So to figure out our domain, it is easiest to look at the equation and determine what is NOT in the domain. We do this by solving $\sqrt{x-6}=0$ and we get x=6 . We now look at values greater than and less than , and we can see that when x<6 , the number under the square root will be negative. When x>6 , the number will be greater than or equal to . Therefore, our domain is anything greater than or equal to 6, or $[6,\infty )$ .

Report an Error

Example Question #55 : Functions

What is the range of y=x^2-4

Possible Answers:

$(-4,\infty )$

$[4,\infty )$

$(-\infty ,-4]$

$(4,\infty )$

$[-4,\infty )$

Correct answer:

$[-4,\infty )$

Explanation:

Because the only term in the equation containing an is squared, we know that its value will range from (when x=0 ) to $\infty$ (as approaches $\infty$ ). When x^2 is large, a constant such as does not matter, but when x^2 is at its smallest, it does. We can see that when x^2=0 , will be at its minimum of . This number gets bracket notation because there is an value such that y=-4 .

Report an Error

Example Question #54 : Functions

What is the domain of the function?

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

Possible Answers:

$(0, \infty)$

$(-\infty, 1)$

$(-\infty, \infty)$

$(-\infty, 0)$

$(1, \infty)$

Correct answer:

$(-\infty, \infty)$

Explanation:

Any value can be inputed in the exponetial.

Report an Error

Example Question #42 : Relations And Functions

Find the domain of the function:

$\frac{1}{\sqrt{x+4}}$

Possible Answers:

$(-\infty,-4]$

$[-4,\infty )$

$(-\infty,-4)$

$(-4,\infty )$

$(-\infty,\infty )$

Correct answer:

$(-4,\infty )$

Explanation:

The square cannot house any negative term or can the denominator be zero. So the lower limit is since cannot be , but any value greater than it is ok. And the upper limit is infinity.

Report an Error

Example Question #61 : Functions

What is the domain for the function?

$f(x) = \frac{\sqrt{2+3x}}{(x+4)(x-2)}$

Possible Answers:

$(-4,-\frac{2}{3}]\cup[-\frac{2}{3},2 )$

$(-4,-\frac{2}{3}]\cup[-\frac{2}{3},2 )\cup(2,\infty )$

$(-\infty,\infty)$

$[-\frac{2}{3},2 )\cup(2,\infty )$

$(-\infty,-4)\cup(-4,-\frac{2}{3}]\cup[-\frac{2}{3},2 )\cup(2,\infty )$

Correct answer:

$[-\frac{2}{3},2 )\cup(2,\infty )$

Explanation:

The denominator becomes when x = -4 or , so the function does not exist at these points. In numerator, must be at least $-\frac{2}{3}$ or greater to be real. So the function is continuous from $-\frac{2}{3}$ to and to any other value greater than .

Report an Error

Example Question #51 : Relations And Functions

What is the domain of the function below?

$\frac{1}{x^2 + 3x + 2}$

Possible Answers:

$(-\infty, -2)\cup(-2,-1)\cup(-1,\infty )$

$(-\infty,\infty )$

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

$(-\infty,1)\cup(1,2)\cup(2,\infty )$

$(-\infty, -2]\cup[-2,-1]\cup[-1,\infty )$

Correct answer:

$(-\infty, -2)\cup(-2,-1)\cup(-1,\infty )$

Explanation:

The denomiator factors out to:

(x+2)(x+1)

The denominator becomes zero when x = -1,-2 . But the function can exist at any other value.

Report an Error

Example Question #1012 : Pre Calculus

What is the domain of the function below?

$\sqrt{3+5x}$

Possible Answers:

$[-3,\infty )$

$[\frac{3}{5},\infty )$

$[-\frac{3}{5},\infty )$

$(-\infty,3 )$

Correct answer:

$[-\frac{3}{5},\infty )$

Explanation:

Cannot have a negative inside the square root. The value of has to be $-\frac{3}{5}$ for the inside of the square root to be at least . This is the lower bound of the domain. Any value of greater than $-\frac{3}{5}$ exists.

Report an Error

Example Question #1016 : Pre Calculus

f(x) = ln((x+2)(x-3))

Possible Answers:

$(-\infty,\infty )$

$(-\infty,-2 )\cup(-2,3 )\cup(3,\infty )$

(-2,3)

$(3,\infty)$

$(-\infty,-2 )\cup(3,\infty )$

Correct answer:

$(-\infty,-2 )\cup(3,\infty )$

Explanation:

The natural log function does not exist if the inside value is negatuve or zero. The points where the inside becomes negative are x = 3 or . If is greater than , both terms, (x+2) and (x-3) , are positive. If is less than , both terms are negative and multiply to become positive. If the value is between and , only one term will be negative and result in a $ln(-\#)$ , which does not exist.

Report an Error

Example Question #64 : Functions

What is the domain of the function?

f(x) = ln(3+x)

Possible Answers:

$[-3,\infty)$

$(\frac{1}{3},\infty)$

$[\frac{1}{3},\infty)$

$(-\infty,\infty)$

$(-3,\infty)$

Correct answer:

$(-3,\infty)$

Explanation:

The value inside a natural log function cannot be negative or . At x = -3 , the inside is and any value less than {-3} cannot be included, because result will be a negative number inside the natural log.

Report an Error

View Pre-Calculus Tutors

James
Certified Tutor

USAF Academy, Bachelors, Astrodynamics and Engineering Sciences. Massachusetts Institute of Technology, Master of Science, Ap...

View Pre-Calculus Tutors

Tara
Certified Tutor

Montclair State University, Bachelor of Science, Mathematics. Montclair State University, Master of Arts, Educational Adminis...

View Pre-Calculus Tutors

Ping
Certified Tutor

The University of Texas at Dallas, Bachelor of Science, Computer Science. University of North Texas, Master of Arts, Education.

All Precalculus Resources

12 Diagnostic Tests 380 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Algebra Tutors in Chicago, GRE Tutors in New York City, LSAT Tutors in Seattle, Computer Science Tutors in New York City, Statistics Tutors in Boston, Algebra Tutors in New York City, GRE Tutors in Chicago, SAT Tutors in San Diego, LSAT Tutors in Denver, ISEE Tutors in Boston

Popular Courses & Classes

ACT Courses & Classes in Los Angeles, ISEE Courses & Classes in Chicago, SSAT Courses & Classes in Miami, Spanish Courses & Classes in Denver, SSAT Courses & Classes in Chicago, ACT Courses & Classes in Chicago, GRE Courses & Classes in Washington DC, Spanish Courses & Classes in Philadelphia, ACT Courses & Classes in Houston, LSAT Courses & Classes in Boston

Popular Test Prep

SSAT Test Prep in Phoenix, ISEE Test Prep in Miami, GMAT Test Prep in Chicago, ACT Test Prep in Los Angeles, ACT Test Prep in Chicago, GRE Test Prep in San Diego, ACT Test Prep in Houston, SSAT Test Prep in Los Angeles, LSAT Test Prep in New York City, LSAT Test Prep in Los Angeles

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

Precalculus : Pre-Calculus

Study concepts, example questions & explanations for Precalculus

All Precalculus Resources

Example Questions

Example Question #54 : Functions

Example Question #44 : Relations And Functions

Example Question #55 : Functions

Example Question #54 : Functions

Example Question #42 : Relations And Functions

Example Question #61 : Functions

Example Question #51 : Relations And Functions

Example Question #1012 : Pre Calculus

Example Question #1016 : Pre Calculus

Example Question #64 : Functions

All Precalculus Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: