Call Now to Set Up Tutoring:

(888) 888-0446

Algebra 1 : Functions and Lines

Study concepts, example questions & explanations for Algebra 1

Create An Account

All Algebra 1 Resources

10 Diagnostic Tests 557 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #665 : Equations Of Lines

Find the midpoint of the line that contains the following endpoints:

(0, 1) and (-2, -5)

Possible Answers:

(-1, -2)

(1, 2)

(1, -3)

(-2, -1)

(2, 1)

Correct answer:

(-1, -2)

Explanation:

When finding the midpoint of a line, we use the following formula

$(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$

where (x_1, y_1) and (x_2, y_2) are the endpoints.

Given the points

(0, 1) and (-2, -5)

we can substitute into the formula. We get

$(\frac{0+-2}{2}, \frac{1+-5}{2})$

$(\frac{0-2}{2}, \frac{1-5}{2})$

$(\frac{-2}{2}, \frac{-4}{2})$

(-1, -2)

Report an Error

Example Question #666 : Equations Of Lines

Find the midpoint of the line containing the following endpoints:

(-1, -1) and (-3, -7)

Possible Answers:

(1, 3)

(-2, -4)

(-1, -3)

(-4, -8)

(2, 4)

Correct answer:

(-2, -4)

Explanation:

When finding the midpoint of a line, we use the following formula

$(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$

where (x_1, y_1) and (x_2, y_2) are the endpoints.

Given the points

(-1, -1) and (-3, -7)

we can substitute into the formula. We get

$(\frac{-1+-3}{2}, \frac{-1+-7}{2})$

$(\frac{-1-3}{2}, \frac{-1-7}{2})$

$(\frac{-4}{2}, \frac{-8}{2})$

(-2, -4)

Report an Error

Example Question #661 : Equations Of Lines

Find the midpoint of the line segment containing the two points

(3,8) and (7,4)

Possible Answers:

(3,6)

(5,6)

(2,2)

(5,4)

Correct answer:

(5,6)

Explanation:

To find the midpoint we follow the formula

$M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

Plugging in the points (3,8) and (7,4) for (x_1,y_1) and (x_2,y_2)

$M=(\frac{3+7}{2},\frac{8+4}{2})$

and we get

(5,6)

Report an Error

Example Question #661 : Equations Of Lines

A line is connected by points (2,5) and (-1,3) on a graph. What is the midpoint?

Possible Answers:

$(-\frac{1}{2},4)$

$(\frac{9}{2},4)$

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

$(-\frac{3}{2},1)$

$(\frac{1}{2},4)$

Correct answer:

$(\frac{1}{2},4)$

Explanation:

Write the midpoint formula.

$(x,y) = (\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$

Let (x_1,y_1) = (2,5) and (x_2,y_2) = (-1,3) .

Substitute the given points.

$(x,y) = (\frac{2+(-1)}{2}, \frac{5+3}{2})$

Simplify the coordinate.

$(x,y) =(\frac{1}{2},4)$

The answer is: $(\frac{1}{2},4)$

Report an Error

Example Question #668 : Equations Of Lines

Find the midpoint between the following two endpoints: (-2,5) and (4,9) .

Possible Answers:

(1,14)

(2,14)

(2,7)

(-3,-2)

(1,7)

Correct answer:

(1,7)

Explanation:

The midpoint formula is $(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})$ . All we need to do is add the x-values and divide by 2, then add the y-values and divide by 2. This leaves us with a midpoint of (1,7) .

Report an Error

Example Question #1 : How To Find Inverse Variation

Find the inverse of the following function:

$f(x) = x^{2}-3$

Possible Answers:

$x^{2} -3$

$x^{2} +3$

None because the given function is not one-to-one.

$\sqrt{x+3}$

$-\sqrt{x+3}$

Correct answer:

None because the given function is not one-to-one.

Explanation:

$f\left ( x \right ) = x^{2}-3$

which is the same as

$y = x^{2}-3$

If we solve for we get

$x^{2} = y +3$

Taking the square root of both sides gives us the following:

$x = \pm \sqrt{y+3}$

Interchanging and gives us

$y = \pm \sqrt{x + 3}$

Which is not one-to-one and therefore not a function.

Report an Error

Example Question #1 : How To Find Inverse Variation

Given

$f\left ( x \right ) = 2x+3$

and

$g\left ( x \right ) = \frac{x-3}{2}$ .

Find $f\left ( g\left ( x \right ) \right )$ .

Possible Answers:

$g\left ( x \right )$

$f\left ( x \right )$

Correct answer:

Explanation:

Starting with $f\left ( x \right ) = 2x+3$

Replace with $g\left ( x \right )$ .

We get the following:

$2\left ( \frac{x-3}{2} \right )+3=x-3+3$

Which is equal to .

Report an Error

Example Question #2 : How To Find Inverse Variation

Given:

f(x)=2x+3

and

$g(x)=\frac{x-3}{2}$ .

Find g(f(x)) .

Possible Answers:

f(x)

g(x)

x+y

Correct answer:

Explanation:

Start with g(x) which is equal to

$\frac{x-3}{2}$

and then replace with f(x) . We get the following:

$\frac{(2x+3)-3}{2}$

which is equal to

$\frac{2x}{2}=x$

Report an Error

Example Question #2 : How To Find Inverse Variation

Which of the following is not a one-to-one function?

$f\left ( x \right ) = 2x + 5$
$f\left ( x \right ) = 2^{-x}$
$f\left ( x \right ) = x^{3} + 5$
$f\left ( x \right ) = \pm \sqrt{x+3}$
$f\left ( x \right ) = x^{5}$

Possible Answers:

Correct answer:

Explanation:

Expression 4 is not even a function because for any value of , one gets two values of violating the definition of a function. If it is not a function, then it can not be an one-to-one function.

Report an Error

Example Question #3 : How To Find Inverse Variation

f(x) is a one-to-one function specified in terms of a set of $\left ( x,y \right )$ coordinates:

A = $\left \{ \left ( 0,0 \right ), \left ( 1,2\right ),\left ( 2,4 \right ), \left ( 3,6 \right )\right \}$

Which one of the following represents the inverse of the function specified by set A?

B = $\left \{ \left ( 0,0 \right ), \left ( 0,1 \right ), \left ( 0,2 \right ), \left ( 0,3 \right ) \right \}$

C = $\left \{ \left ( 0,0 \right ), \left ( 2,1 \right ), \left ( 4,2 \right ), \left ( 6,3 \right ) \right \}$

D = $\left \{ \left ( 1,1 \right ), \left ( 2,1 \right ), \left ( -2,1 \right ), \left ( 3,1 \right ) \right \}$

E = $\left \{ \left ( -2,1 \right ), \left ( -2,5 \right ), \left ( -2,3 \right ), \left ( -2, -2 \right ) \right \}$

F = $\left \{ \left ( 2,0 \right ), \left ( 2,-3 \right ),\left ( 2,5 \right ), \left ( 2,-7 \right ) \right \}$

Possible Answers:

Set E

Set F

Set C

Set D

Set B

Correct answer:

Set C

Explanation:

The set A is an one-to-one function of the form

f(x) = 2x

One can find $f^{-1}\left ( x \right )$ by interchanging the and coordinates in set A resulting in set C.

Report an Error

View Algebra Tutors

Jeffrey
Certified Tutor

View Algebra Tutors

Sydney
Certified Tutor

University of Vermont, Bachelor of Science, Nursing (RN). University of Connecticut, Bachelor of Science, Health Sciences, Ge...

View Algebra Tutors

Mark
Certified Tutor

Rochester Institute of Technology, Bachelor of Science, Game and Interactive Media Design. Rochester Institute of Technology,...

All Algebra 1 Resources

10 Diagnostic Tests 557 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

MCAT Tutors in Boston, Math Tutors in Miami, Algebra Tutors in Philadelphia, Chemistry Tutors in Chicago, ISEE Tutors in Houston, GRE Tutors in San Francisco-Bay Area, LSAT Tutors in Denver, SAT Tutors in Washington DC, Algebra Tutors in Chicago, GMAT Tutors in Houston

Popular Courses & Classes

Spanish Courses & Classes in Atlanta, GMAT Courses & Classes in Boston, ISEE Courses & Classes in Atlanta, SAT Courses & Classes in New York City, Spanish Courses & Classes in Philadelphia, ACT Courses & Classes in Denver, GRE Courses & Classes in New York City, GRE Courses & Classes in Washington DC, SAT Courses & Classes in San Diego, GRE Courses & Classes in Chicago

Popular Test Prep

GRE Test Prep in Miami, SAT Test Prep in Chicago, SAT Test Prep in Phoenix, GRE Test Prep in Washington DC, MCAT Test Prep in New York City, LSAT Test Prep in Atlanta, ISEE Test Prep in Washington DC, GRE Test Prep in Denver, GMAT Test Prep in Los Angeles, LSAT Test Prep in Chicago

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

Algebra 1 : Functions and Lines

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #665 : Equations Of Lines

Example Question #666 : Equations Of Lines

Example Question #661 : Equations Of Lines

Example Question #661 : Equations Of Lines

Example Question #668 : Equations Of Lines

Example Question #1 : How To Find Inverse Variation

Example Question #1 : How To Find Inverse Variation

Example Question #2 : How To Find Inverse Variation

Example Question #2 : How To Find Inverse Variation

Example Question #3 : How To Find Inverse Variation

All Algebra 1 Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: