Common Core: High School - Functions : Function and Graph Relationships: CCSS.Math.Content.HSF-IF.B.4

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Example Question #11 : Function And Graph Relationships: Ccss.Math.Content.Hsf If.B.4

Find the axis of symmetry for the following function.

Possible Answers:

Correct answer:

Explanation:

This question is testing one's ability to grasp the relationship between a function algebraically, and the image it creates graphically. Problems like these are considered modeling problems because of their application. For example, the intercepts, extreme values, slope, symmetry, and end behavior for these functions mark key relationships between the inputs and the resulting outputs. 

For the purpose of Common Core Standards, application of interpreting functions fall within the Cluster B of the function and use of function notation concept (CCSS.MATH.CONTENT.HSF-IF.B). 

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify what the question is asking.

This particular question is asking for the axis of symmetry for this particular function.

Step 2: Determine the approach to solve the problem.

      I. Graphically plot the function using computer technology or graphing calculator.

         Then, find the vertical line that splits the graph into two mirrored images. In other words, find the vertical line that represents a vertical asymptote and the horizontal line that represents a horizontal asymptotes.

Step 3: Graph the function and plot the vertical line that is equal to the  value of the vertical line that represents a vertical asymptote and the  value that is the horizontal line that represents a horizontal asymptotes.

Screen shot 2016 01 11 at 2.03.32 pm

Step 4: Answer the question.

The vertical asymptote occurs at   and the horizontal asymptote occurs at  thus making them both axis of symmetry for the given function.

Example Question #12 : Function And Graph Relationships: Ccss.Math.Content.Hsf If.B.4

Given the function , what is the  intercept?

Possible Answers:

Correct answer:

Explanation:

This question is testing one's ability to grasp the relationship between a function algebraically, and the image it creates graphically. Problems like these are considered modeling problems because of their application. For example, the intercepts, extreme values, slope, symmetry, and end behavior for these functions mark key relationships between the inputs and the resulting outputs. 

For the purpose of Common Core Standards, application of interpreting functions fall within the Cluster B of the function and use of function notation concept (CCSS.MATH.CONTENT.HSF-IF.B). 

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify what the question is asking.

This particular question is asking for the  intercept of the function.

Step 2: Determine the approach to solve the problem.

      I. Graphically plot the function using computer technology or graphing calculator.

         Then, find where the graph intersects the -axis.

     II. Algebraically, find the intercepts by substituting in zero for  and solving for  (calculating the -intercept).

Step 3: Choose an approach from Step 2 and perform the necessary actions.

For the purpose of this question let's solve using option I.

Screen shot 2016 01 12 at 10.27.05 am

Looking at the graph above, the function crosses the -axis at twelve. Therefore, the -intercept is 12.

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All Common Core: High School - Functions Resources

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