Call Now to Set Up Tutoring:

(888) 888-0446

HiSET: Math : Estimate rate of change from a graph

Study concepts, example questions & explanations for HiSET: Math

Create An Account

All HiSET: Math Resources

125 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Estimate Rate Of Change From A Graph

Estimate slope

The graph of a function is given above, with the coordinates of two points on the curve shown. Use the coordinates given to approximate the rate of change of the function between the two points.

Possible Answers:

$\frac{3}{5}$

$-\frac{11}{7}$

$\frac{7}{11}$

$\frac{5}{3}$

$-\frac{3}{5}$

Correct answer:

$\frac{3}{5}$

Explanation:

The rate of change between two points on a curve can be approximated by calculating the change between two points.

Let (x_1,y_1) be the coordinates of the first point and (x_2,y_2) be the coordinates of the second point. Then the formula giving approximate rate of change is:

$\frac{y_2 - y_1} {x_2 - x_1}$

Notice that the numerator is the overall change in y, and the denominator is the overall change in x.

The calculation for the problem proceeds as follows:

Let (3,2) be the first point and (8,5) be the second point. Substitute in the values from these coordinates:

$\frac{y_2 - y_1} {x_2 - x_1} \rightarrow \frac {5-2}{8-3}$

Subtract to get the final answer:

$\frac{3}{5}$

Note that it does not matter which you assign to be the first point and which you assign to be the second, as it will lead to the same value due to negatives canceling out.

Report an Error

Example Question #1 : Estimate Rate Of Change From A Graph

Graph 1

Above is the graph of a function . Estimate the rate of change of on the interval [-2, -1.5]

Possible Answers:

Correct answer:

Explanation:

The rate of change of a function on the interval [a, b] is equal to

$r = \frac{f(b)-f(a)}{b - a}$ .

Set a = -2, b = -1.5 . Refer to the graph of the function below:

Graph 1

The graph passes through (-2, 2) and (-1.5, 5) .

f(-2) = 2 , f(-1.5)= 5 . Thus,

$r = \frac{f(-1.5)-f(-2)}{-1.5 - (-2)} = \frac{5-2}{0.5} = \frac{3}{0.5} = 6$ ,

the correct response.

Report an Error

Example Question #3 : Rate Of Change Of A Function

Graph 1

Above is the graph of a function , which is defined and continuous on $(-\infty, \infty)$ . The average rate of change of on the interval [1, 5] is 4. Estimate f(5) .

Possible Answers:

Correct answer:

Explanation:

The rate of change of a function on the interval [a, b] is equal to

$r = \frac{f(b)-f(a)}{b - a}$ .

Set a = 1, b = 5, r =4 . Examine the figure below:

Graph 1

The graph passes through the point (1, 2) , so f(1) = 2 . Therefore,

$4 = \frac{f(5)-f(1)}{5-1}$

and, substituting,

$4 = \frac{f(5)-2}{4}$

Solve for f(5) using algebra:

$\frac{f(5)-2}{4} \cdot 4 = 4 \cdot 4$

f(5)-2 =16

f(5)-2+ 2 =16 + 2

f(5)= 18 ,

the correct response.

Report an Error

Example Question #1 : Estimate Rate Of Change From A Graph

Graph 1

Above is the graph of a function. The average rate of change of over the interval (0, c) is $-\frac{4}{5}$ . Which of these values comes closest to being a possible value of ?

Possible Answers:

Correct answer:

Explanation:

The average rate of change of a function on the interval (a, b) is equal to

$r = \frac{f(b)-f(a)}{b - a}$ .

Restated, it is the slope of the line that passes through (a, f(a)) and (b, f(b)) .

To find the correct value of that answers this question, it suffices to examine the line with slope $-\frac{4}{5}$ through (0, f(0)) and find the point among those given that is closest to the line. This line falls 4 units for every 5 horizontal units, so the line looks like this:

Graph 1

The -coordinate of the point of intersection is closer to 2 than to any other of the values in the other four choices. This makes 2 the correct choice.

Report an Error

View Tutors

Margaret
Certified Tutor

Smith College, Bachelor of Science, Biological and Physical Sciences.

View Tutors

Samir
Certified Tutor

University of South Florida-Main Campus, Master of Fine Arts, Studio Arts.

View Tutors

Grace
Certified Tutor

University of Massachusetts-Dartmouth, Bachelor of Education, Portuguese. University of Massachusetts-Dartmouth, Masters in B...

All HiSET: Math Resources

125 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

MCAT Tutors in Boston, Chemistry Tutors in Miami, Algebra Tutors in Seattle, Physics Tutors in Chicago, Math Tutors in Chicago, Biology Tutors in New York City, LSAT Tutors in Washington DC, Computer Science Tutors in Los Angeles, Algebra Tutors in Los Angeles, Math Tutors in San Diego

Popular Courses & Classes

GRE Courses & Classes in San Diego, ACT Courses & Classes in Dallas Fort Worth, SAT Courses & Classes in Dallas Fort Worth, SSAT Courses & Classes in San Diego, ACT Courses & Classes in Washington DC, LSAT Courses & Classes in New York City, GMAT Courses & Classes in Denver, ACT Courses & Classes in Miami, LSAT Courses & Classes in Houston, ACT Courses & Classes in Phoenix

Popular Test Prep

MCAT Test Prep in Houston, ACT Test Prep in Dallas Fort Worth, MCAT Test Prep in San Francisco-Bay Area, ACT Test Prep in Washington DC, MCAT Test Prep in Chicago, GMAT Test Prep in Seattle, GRE Test Prep in Phoenix, ISEE Test Prep in Miami, ISEE Test Prep in Atlanta, SAT Test Prep in New York City

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

HiSET: Math : Estimate rate of change from a graph

Study concepts, example questions & explanations for HiSET: Math

All HiSET: Math Resources

Example Questions

Example Question #1 : Estimate Rate Of Change From A Graph

Example Question #1 : Estimate Rate Of Change From A Graph

Example Question #3 : Rate Of Change Of A Function

Example Question #1 : Estimate Rate Of Change From A Graph

All HiSET: Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: