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All Common Core: High School - Functions Resources

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Flashcards: Function and Graph Relationships: CCSS.Math.Content.HSF-IF.B.4

Given the function , find the and intercepts.

$f(x)=\frac{x}{3}+2x-1$

$\\ \textup{y-intercept: }-1 \\ \\ \textup{x-intercept: }\frac{3}{7}$

$\\ \textup{y-intercept: 1} \\ \\ \textup{x-intercept: }\frac{4}{7}$

$\\ \textup{y-intercept: 1} \\ \\ \textup{x-intercept: }\frac{3}{7}$

$\\ \textup{y-intercept: 1} \\ \\ \textup{x-intercept: }\frac{1}{7}$

$\\ \textup{y-intercept: }-1 \\ \\ \textup{x-intercept: }-\frac{3}{7}$

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Flashcards: Function and Graph Relationships: CCSS.Math.Content.HSF-IF.B.4

Given the function , find the and intercepts.

$f(x)=\frac{x}{3}+2x-1$

Your answer:

$\\ \textup{y-intercept: }-1 \\ \\ \textup{x-intercept: }\frac{3}{7}$

Your answer:

$\\ \textup{y-intercept: 1} \\ \\ \textup{x-intercept: }\frac{4}{7}$

Your answer:

$\\ \textup{y-intercept: 1} \\ \\ \textup{x-intercept: }\frac{1}{7}$

Your answer:

$\\ \textup{y-intercept: }-1 \\ \\ \textup{x-intercept: }-\frac{3}{7}$

Correct answer:

$\\ \textup{y-intercept: 1} \\ \\ \textup{x-intercept: }\frac{3}{7}$

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 and intercepts 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 and where it intersects the -axis as these correspond to the intercepts.

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

To algebraically solve for the -intercept substitute zero in for and solve for . (Recall that f(x)=y )

$\\ f(x)=\frac{x}{3}+2x-1 \\ \\y=\frac{x}{3}+2x-1\\ \\ 0=\frac{x}{3}+2x-1$

Perform algebraic operations to combine like terms.

$\\ 0=\frac{1}{3}x+\frac{6}{3}x-1 \\ \\0=\frac{7}{3}x-1$

Isolate the variable on one side of the equation by using the opposite operation to move all other constants to the other side.

$\\0+1=\frac{7}{3}x-1+1 \\ \\1=\frac{7}{3}x \\ \\ \frac{3}{7}\cdot 1=\frac{3}{7}\cdot \frac{7}{3}x \\ \\\frac{3}{7}=x$

To algebraically solve for the -intercept substitute zero in for and solve for . (Recall that f(x)=y )

$\\f(x)=\frac{x}{3}+2x-1 \\ \\f(0)=\frac{0}{3}+2(0)-1 \\ \\f(0)=-1 \\ \\y=-1$

Step 4: Answer question.

Using the algebraic approach, the and intercepts were found to be as follows.

$\\ \textup{y-intercept: 1};\ \textup{x-intercept: }\frac{3}{7}$

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All Common Core: High School - Functions Resources

Flashcards: Function and Graph Relationships: CCSS.Math.Content.HSF-IF.B.4

Flashcards: Function and Graph Relationships: CCSS.Math.Content.HSF-IF.B.4

Flashcards: Function and Graph Relationships: CCSS.Math.Content.HSF-IF.B.4

Flashcards: Function and Graph Relationships: CCSS.Math.Content.HSF-IF.B.4

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