We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Common Core: High School - Functions : Compare Function Properties: CCSS.Math.Content.HSF-IF.C.9

Study concepts, example questions & explanations for Common Core: High School - Functions

Create An Account

All Common Core: High School - Functions Resources

6 Diagnostic Tests 82 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Compare Function Properties: Ccss.Math.Content.Hsf If.C.9

$\textup{ Table 1} \\\\ \begin{tabular}{||c c||} \hline Time & Distance \\ [0.5ex] \hline\hline 0&0 \\ 1&4 \\ 2&6 \\ 2.5 & 6.25 \\ 3&6\\ 4&4 \\ 5&0\\ \hline \hline \end{tabular}$ Screen shot 2016 01 13 at 7.10.56 pm

The above table and figure describe two different particle's travel over time. Which particle has a larger maximum?

Possible Answers:

$\textup{Figure 1}$

$\textup{Figure 1 and Table 1 are equal.}$

$\text{No maximum exists. }$

$\textup{Table 1}$

$\textup{More information is needed.}$

Correct answer:

$\textup{Figure 1}$

Explanation:

This question is testing one's ability to compare the properties of functions when they are illustrated in different forms. This question specifically is asking for the examination and interpretation of two quadratic functions for which one is illustrated in a table format and the other is illustrated graphically.

For the purpose of Common Core Standards, "Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions)." falls within the Cluster C of "Analyze Functions Using Different Representations" concept (CCSS.MATH.CONTENT.HSF-IF.C.9).

Step 1: Identify the maximum of Table 1.

Using the table find the time value where the largest distance exists.

$\textup{ Table 1} \\\\ \begin{tabular}{||c c||} \hline Time & Distance \\ [0.5ex] \hline\hline 0&0 \\ 1&4 \\ 2&6 \\ {\color{Red} 2.5} & {\color{Red} 6.25} \\ 3&6\\ 4&4 \\ 5&0\\ \hline \hline \end{tabular}$

Now, let us plot the points from the table and connect them with a smooth curve to represent the function.

Screen shot 2016 01 13 at 7.03.33 pm

It is seen from the table and the graph that the vertex or maximum of the function exists at (2.5,6.25) .

Step 2: Identify the maximum of Figure 2.

Screen shot 2016 01 13 at 7.10.56 pm

Looking at Figure 1, plotting the vertex and extending a vertical and horizontal line, we can find the coordinate pair of the vertex.

Therefore the vertex or maximum of Figure 1 is (2.5,9.25) .

Step 3: Compare the maximums from step 1 and step 2.

Compare the value coordinate from both maximums.

$6.25<9.25\Rightarrow \textup{Table 1}< \textup{Figure 1}$

Therefore, Figure 1 has the largest maximum.

Report an Error

Example Question #2 : Compare Function Properties: Ccss.Math.Content.Hsf If.C.9

$\begin{tabular}{||c c||} \hline Time & Distance \\ [0.5ex] \hline\hline 0&0 \\ 1&4 \\ 2&6 \\ 2.5 & 6.25 \\ 3&6\\ 4&4 \\ 5&0\\ \hline \hline \end{tabular}$

The table and graph describe two different particle's travel over time. Which particle has a larger maximum?

Possible Answers:

$\text{The table and graph have the same maximum.}$

$\text{No maximum exists. }$

$\text{More information is needed.}$

$\text{Graph}$

$\text{Table}$

Correct answer:

$\text{Table}$

Explanation:

Step 1: Identify the maximum of Table 1.

Using the table find the time value where the largest distance exists.

$\begin{tabular}{||c c||} \hline Time & Distance \\ [0.5ex] \hline\hline 0&0 \\ 1&4 \\ 2&6 \\ {\color{Red} 2.5} & {\color{Red} 6.25} \\ 3&6\\ 4&4 \\ 5&0\\ \hline \hline \end{tabular}$

Recall that the time represents the values while the distance represents the values. Therefore the ordered pair for the maximum can be written as (2.5,6.25) .

Step 2: Identify the maximum of the graph

Recall that the maximum of a parabola opening down, occurs at the peak where the vertex lies.

For this particular graph the vertex is at (2,3) .

Step 3: Compare the maximums from step 1 and step 2.

Compare the value coordinate from both maximums.

$3<6.25\Rightarrow \textup{Graph}< \textup{Table}$

Therefore, the table has the largest maximum.

Report an Error

Example Question #3 : Compare Function Properties: Ccss.Math.Content.Hsf If.C.9

$\begin{tabular}{||c c||} \hline Time & Distance \\ [0.5ex] \hline\hline 0&0 \\ 1&4 \\ 2&6 \\ 2.5 & 6.25 \\ 3&6\\ 4&4 \\ 5&0\\ \hline \hline \end{tabular}$

The table and graph describe two different particle's travel over time. Which particle has a larger maximum?

Possible Answers:

$\text{No maximum exists. }$

$\text{Graph and Table}$

$\text{Graph}$

$\textup{More information is needed.}$

$\text{Table}$

Correct answer:

$\text{Table}$

Explanation:

Step 1: Identify the maximum of Table 1.

Using the table find the time value where the largest distance exists.

$\begin{tabular}{||c c||} \hline Time & Distance \\ [0.5ex] \hline\hline 0&0 \\ 1&4 \\ 2&6 \\ {\color{Red} 2.5} & {\color{Red} 6.25} \\ 3&6\\ 4&4 \\ 5&0\\ \hline \hline \end{tabular}$

Recall that the time represents the values while the distance represents the values. Therefore the ordered pair for the maximum can be written as (2.5,6.25) .

Step 2: Identify the maximum of the graph

Recall that the maximum of a cubic function is known as a local maximum. This occurs at the vertex of the peak on the graph which in this particular case, is at the point (-1,1) .

Step 3: Compare the maximums from step 1 and step 2.

Compare the value coordinate from both maximums.

$1<6.25\Rightarrow \textup{Graph}< \textup{Table}$

Therefore, the table has the largest maximum.

Report an Error

Example Question #2 : Compare Function Properties: Ccss.Math.Content.Hsf If.C.9

$\begin{tabular}{||c c||} \hline Time & Distance \\ [0.5ex] \hline\hline 0&10 \\ 1&4 \\ 2&3 \\ 2.5 & 1 \\ 3&3\\ 4&4 \\ 5&10\\ \hline \hline \end{tabular}$

The table and graph describe two different particle's travel over time. Which particle has a lower minimum?

Possible Answers:

$\text{Table}$

$\text{No minimum exists}$

$\text{Table and Graph are equal}$

$\text{Graph}$

$\text{More information is needed}$

Correct answer:

$\text{Graph}$

Explanation:

Step 1: Identify the minimum of the table.

Using the table find the time value where the lowest distance exists.

$\begin{tabular}{||c c||} \hline Time & Distance \\ [0.5ex] \hline\hline 0&10 \\ 1&4 \\ 2&3 \\ {\color{Red} 2.5} & {\color{Red} 1} \\ 3&3\\ 4&4 \\ 5&10\\ \hline \hline \end{tabular}$

Recall that the time represents the values while the distance represents the values. Therefore the ordered pair for the minimum can be written as (2.5,1) .

Step 2: Identify the minimum of the graph

Recall that the minimum of a cubic function is known as a local minimum. This occurs at the valley where the vertex lies.

For this particular graph the vertex is at (1,-3) .

Step 3: Compare the minimums from step 1 and step 2.

Compare the value coordinate from both minimums.

$-3<1\Rightarrow \textup{Graph}< \textup{Table}$

Therefore, the graph has the lowest minimum.

Report an Error

Example Question #5 : Compare Function Properties: Ccss.Math.Content.Hsf If.C.9

$\begin{tabular}{||c c||} \hline Time & Distance \\ [0.5ex] \hline\hline 0&12 \\ 1&9 \\ 2&7 \\ 2.5 & 6.25 \\ 3&7\\ 4&9 \\ 5&12\\ \hline \hline \end{tabular}$

The table and graph describe two different particle's travel over time. Which particle has a lower minimum?

Possible Answers:

$\text{Table}$

$\text{Graph}$

$\text{Graph and Table}$

$\text{More information is needed.}$

$\text{There is no minimum.}$

Correct answer:

$\text{Graph}$

Explanation:

Step 1: Identify the minimum of the table.

Using the table find the time value where the lowest distance exists.

$\begin{tabular}{||c c||} \hline Time & Distance \\ [0.5ex] \hline\hline 0&12 \\ 1&9 \\ 2&7 \\ {\color{Red} 2.5} & {\color{Red}6.25} \\ 3&7\\ 4&9 \\ 5&12\\ \hline \hline \end{tabular}$

Recall that the time represents the values while the distance represents the values. Therefore the ordered pair for the minimum can be written as (2.5,6.25) .

Step 2: Identify the minimum of the graph

Recall that the minimum of a parabola opening up, occurs at the valley where the vertex lies.

For this particular graph the vertex is at (4,3) .

Step 3: Compare the minimums from step 1 and step 2.

Compare the value coordinate from both minimums.

$3<6.25\Rightarrow \textup{Graph}< \textup{Table}$

Therefore, the graph has the lowest minimum.

Report an Error

Example Question #6 : Compare Function Properties: Ccss.Math.Content.Hsf If.C.9

$\begin{tabular}{||c c||} \hline Time & Distance \\ [0.5ex] \hline\hline 0&0 \\ 1&4 \\ 2&6 \\ 2.5 & 6.25 \\ 3&6\\ 4&4 \\ 5&0\\ \hline \hline \end{tabular}$

The table and graph describe two different particle's travel over time. Which particle has a larger maximum?

Possible Answers:

$\text{More information is needed}$

$\text{Table}$

$\text{No maximum exists}$

$\text{Table and Graph are equal}$

$\text{Graph}$

Correct answer:

$\text{Table}$

Explanation:

Step 1: Identify the maximum of Table 1.

Using the table find the time value where the largest distance exists.

$\begin{tabular}{||c c||} \hline Time & Distance \\ [0.5ex] \hline\hline 0&0 \\ 1&4 \\ 2&6 \\ {\color{Red} 2.5} & {\color{Red} 6.25} \\ 3&6\\ 4&4 \\ 5&0\\ \hline \hline \end{tabular}$

Recall that the time represents the values while the distance represents the values. Therefore the ordered pair for the maximum can be written as (2.5,6.25) .

Step 2: Identify the maximum of the graph

Recall that the maximum of a cubic function is known as a local maximum. This occurs at the vertex of the peak on the graph which in this particular case, is at the point (-1.25,4.25) .

Step 3: Compare the maximums from step 1 and step 2.

Compare the value coordinate from both maximums.

$4.25<6.25\Rightarrow \textup{Graph}< \textup{Table}$

Therefore, the table has the largest maximum.

Report an Error

Example Question #7 : Compare Function Properties: Ccss.Math.Content.Hsf If.C.9

$\begin{tabular}{||c c||} \hline Time & Distance \\ [0.5ex] \hline\hline 0&0 \\ 1&4 \\ 2&6 \\ 2.5 & 6.25 \\ 3&6\\ 4&4 \\ 5&0\\ \hline \hline \end{tabular}$

The table and graph describe two different particle's travel over time. Which particle has a larger maximum?

Possible Answers:

$\text{Table and graph are equal}$

$\text{More information is needed.}$

$\text{No maximum exists.}$

$\text{Graph}$

$\text{Table}$

Correct answer:

$\text{Table}$

Explanation:

Step 1: Identify the maximum of Table 1.

Using the table find the time value where the largest distance exists.

$\begin{tabular}{||c c||} \hline Time & Distance \\ [0.5ex] \hline\hline 0&0 \\ 1&4 \\ 2&6 \\ {\color{Red} 2.5} & {\color{Red} 6.25} \\ 3&6\\ 4&4 \\ 5&0\\ \hline \hline \end{tabular}$

Recall that the time represents the values while the distance represents the values. Therefore the ordered pair for the maximum can be written as (2.5,6.25) .

Step 2: Identify the maximum of the graph

Recall that the maximum of a parabola occurs at the vertex of the peak on the graph which in this particular case, is at the point (0,3)

Step 3: Compare the maximums from step 1 and step 2.

Compare the value coordinate from both maximums.

$3<6.25\Rightarrow \textup{Graph}< \textup{Table}$

Therefore, the table has the largest maximum.

Report an Error

Example Question #8 : Compare Function Properties: Ccss.Math.Content.Hsf If.C.9

$\begin{tabular}{||c c||} \hline Time & Distance \\ [0.5ex] \hline\hline 0&0 \\ 1&4 \\ 2&6 \\ 2.5 & 6.25 \\ 3&6\\ 4&4 \\ 5&0\\ \hline \hline \end{tabular}$

The table and graph describe two different particle's travel over time. Which particle has a larger maximum?

Possible Answers:

$\text{More information is needed.}$

$\text{Graph}$

$\text{Table}$

$\text{Table and graph are equal}$

$\text{No maximum exists.}$

Correct answer:

$\text{Table}$

Explanation:

Step 1: Identify the maximum of Table 1.

Using the table find the time value where the largest distance exists.

$\begin{tabular}{||c c||} \hline Time & Distance \\ [0.5ex] \hline\hline 0&0 \\ 1&4 \\ 2&6 \\ {\color{Red} 2.5} & {\color{Red} 6.25} \\ 3&6\\ 4&4 \\ 5&0\\ \hline \hline \end{tabular}$

Recall that the time represents the values while the distance represents the values. Therefore the ordered pair for the maximum can be written as (2.5,6.25) .

Step 2: Identify the maximum of the graph

Recall that the maximum of a parabola occurs at the vertex of the peak on the graph which in this particular case, is at the point (4,5)

Step 3: Compare the maximums from step 1 and step 2.

Compare the value coordinate from both maximums.

$5<6.25\Rightarrow \textup{Graph}< \textup{Table}$

Therefore, the table has the largest maximum.

Report an Error

Example Question #9 : Compare Function Properties: Ccss.Math.Content.Hsf If.C.9

$\begin{tabular}{||c c||} \hline Time & Distance \\ [0.5ex] \hline\hline 0&12 \\ 1&9 \\ 2&7 \\ 2.5 & 6.25 \\ 3&7\\ 4&9 \\ 5&12\\ \hline \hline \end{tabular}$

The table and graph describe two different particle's travel over time. Which particle has a lower minimum?

Possible Answers:

$\text{More information is needed}$

$\text{Graph and table are equal}$

$\text{Graph}$

$\text{Table}$

$\text{No minimum is exists}$

Correct answer:

$\text{Graph}$

Explanation:

Step 1: Identify the minimum of the table.

Using the table find the time value where the lowest distance exists.

$\begin{tabular}{||c c||} \hline Time & Distance \\ [0.5ex] \hline\hline 0&12 \\ 1&9 \\ 2&7 \\ {\color{Red} 2.5} & {\color{Red} 6.25} \\ 3&7\\ 4&9 \\ 5&12\\ \hline \hline \end{tabular}$

Recall that the time represents the values while the distance represents the values. Therefore the ordered pair for the minimum can be written as (2.5,6.25) .

Step 2: Identify the minimum of the graph

Recall that the minimum of a parabola opening up occurs at the valley where the vertex lies.

For this particular graph the vertex is at (4,5) .

Step 3: Compare the minimums from step 1 and step 2.

Compare the value coordinate from both minimums.

$5<6.25\Rightarrow \textup{Graph}< \textup{Table}$

Therefore, the graph has the lowest minimum.

Report an Error

Example Question #10 : Compare Function Properties: Ccss.Math.Content.Hsf If.C.9

$\begin{tabular}{||c c||} \hline Time & Distance \\ [0.5ex] \hline\hline 0&0 \\ 1&4 \\ 2&6 \\ 2.5 & 6.25 \\ 3&6\\ 4&4 \\ 5&0\\ \hline \hline \end{tabular}$ Q10

The table and graph describe two different particle's travel over time. Which particle has a larger maximum?

Possible Answers:

$\text{Table}$

$\text{Graph}$

$\text{Table and graph are equal}$

$\text{No maximum exists}$

$\text{More information is needed}$

Correct answer:

$\text{Table}$

Explanation:

Step 1: Identify the maximum of Table 1.

Using the table find the time value where the largest distance exists.

$\begin{tabular}{||c c||} \hline Time & Distance \\ [0.5ex] \hline\hline 0&0 \\ 1&4 \\ 2&6 \\ {\color{Red} 2.5} & {\color{Red} 6.25} \\ 3&6\\ 4&4 \\ 5&0\\ \hline \hline \end{tabular}$

Recall that the time represents the values while the distance represents the values. Therefore the ordered pair for the maximum can be written as (2.5,6.25) .

Step 2: Identify the maximum of the graph

Recall that the maximum of a cubic function is known as a local maximum. This occurs at the vertex of the peak on the graph which in this particular case, is at the point (1,1) .

Q10

Step 3: Compare the maximums from step 1 and step 2.

Compare the value coordinate from both maximums.

$1<6.25\Rightarrow \textup{Graph}< \textup{Table}$

Therefore, the table has the largest maximum.

Report an Error

View Tutors

Joshua
Certified Tutor

Murray State University, Bachelor in Arts, Spanish. Lipscomb University, Bachelor of Science, Teacher Assistant.

View Tutors

Kaylee
Certified Tutor

Brigham Young University, Bachelor, MFA - Animation.

View Tutors

Lydia
Certified Tutor

The Richard Stockton College of New Jersey, Bachelor of Science, Biochemistry and Molecular Biology.

All Common Core: High School - Functions Resources

6 Diagnostic Tests 82 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Biology Tutors in Boston, ACT Tutors in Miami, LSAT Tutors in Atlanta, SSAT Tutors in Chicago, Calculus Tutors in Seattle, ACT Tutors in Denver, Calculus Tutors in New York City, Statistics Tutors in Denver, Algebra Tutors in Miami, English Tutors in Houston

Popular Courses & Classes

SAT Courses & Classes in Los Angeles, GRE Courses & Classes in Boston, GMAT Courses & Classes in Miami, SAT Courses & Classes in New York City, ACT Courses & Classes in Philadelphia, GMAT Courses & Classes in Philadelphia, LSAT Courses & Classes in Philadelphia, ACT Courses & Classes in Boston, GMAT Courses & Classes in Phoenix, GMAT Courses & Classes in Dallas Fort Worth

Popular Test Prep

LSAT Test Prep in Dallas Fort Worth, SAT Test Prep in New York City, SSAT Test Prep in Denver, MCAT Test Prep in Atlanta, GRE Test Prep in Denver, GMAT Test Prep in Philadelphia, GRE Test Prep in Philadelphia, MCAT Test Prep in New York City, ACT Test Prep in Denver, GMAT Test Prep in Miami

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

Common Core: High School - Functions : Compare Function Properties: CCSS.Math.Content.HSF-IF.C.9

Study concepts, example questions & explanations for Common Core: High School - Functions

All Common Core: High School - Functions Resources

Example Questions

Example Question #1 : Compare Function Properties: Ccss.Math.Content.Hsf If.C.9

Example Question #2 : Compare Function Properties: Ccss.Math.Content.Hsf If.C.9

Example Question #3 : Compare Function Properties: Ccss.Math.Content.Hsf If.C.9

Example Question #2 : Compare Function Properties: Ccss.Math.Content.Hsf If.C.9

Example Question #5 : Compare Function Properties: Ccss.Math.Content.Hsf If.C.9

Example Question #6 : Compare Function Properties: Ccss.Math.Content.Hsf If.C.9

Example Question #7 : Compare Function Properties: Ccss.Math.Content.Hsf If.C.9

Example Question #8 : Compare Function Properties: Ccss.Math.Content.Hsf If.C.9

Example Question #9 : Compare Function Properties: Ccss.Math.Content.Hsf If.C.9

Example Question #10 : Compare Function Properties: Ccss.Math.Content.Hsf If.C.9

All Common Core: High School - Functions Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: