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All Common Core: High School - Functions Resources

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Flashcards: Graph Square Root, Cube Root, and Piecewise Functions: CCSS.Math.Content.HSF-IF.C.7b

Graph the following function

$f(x)=\sqrt{x+4}$

Screen shot 2016 01 12 at 3.00.23 pm

Screen shot 2016 01 13 at 9.26.23 am

Screen shot 2016 01 13 at 9.25.36 am

Screen shot 2016 01 13 at 9.26.03 am

Screen shot 2016 01 13 at 9.26.38 am

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Flashcards: Graph Square Root, Cube Root, and Piecewise Functions: CCSS.Math.Content.HSF-IF.C.7b

Graph the following function

$f(x)=\sqrt{x+4}$

Your answer:

Screen shot 2016 01 13 at 9.26.23 am

Your answer:

Screen shot 2016 01 13 at 9.25.36 am

Your answer:

Screen shot 2016 01 13 at 9.26.03 am

Your answer:

Screen shot 2016 01 13 at 9.26.38 am

Correct answer:

Screen shot 2016 01 12 at 3.00.23 pm

Explanation:

This question tests one's ability to graph a square root function.

For the purpose of Common Core Standards, "graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions" falls within the Cluster C of "Analyze Functions Using Different Representations" concept (CCSS.MATH.CONTENT.HSF-IF.C.7).

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: Make a table of (x,y) coordinates for the function.

$\begin{tabular}{ |c|c|c|c| } \hline x & f(x) & y \\ \hline -4& f(-4) & 0 \\ 0 & f(0) & 2 \\ 5&f(5)& 3\\ \hline \end{tabular}$

The values in the table are found by substituting in the x values into the function as follows.

$\\f(-4)=\sqrt{-4+4}=\sqrt{0}=0 \\f(0)=\sqrt{0+4}=\sqrt{4}=2 \\f(5)=\sqrt{5+4}=\sqrt{9}=3$

Step 2: Plot the points on a coordinate grid

Screen shot 2016 01 13 at 9.20.36 am

Step 3: Connect the points with a smooth curve.

Recall that a square root function cannot have negative values under the radical therefore, no x values less than negative four will be in the domain.

Screen shot 2016 01 12 at 3.00.23 pm

Flashcards: Graph Square Root, Cube Root, and Piecewise Functions: CCSS.Math.Content.HSF-IF.C.7b

Graph the following function.

$f(x)=\sqrt{-x+2}$

Screen shot 2016 01 12 at 3.00.23 pm

Screen shot 2016 01 13 at 9.26.03 am

Screen shot 2016 01 13 at 9.25.36 am

Screen shot 2016 01 23 at 8.33.58 am

Screen shot 2016 01 13 at 9.26.38 am

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Flashcards: Graph Square Root, Cube Root, and Piecewise Functions: CCSS.Math.Content.HSF-IF.C.7b

Graph the following function.

$f(x)=\sqrt{-x+2}$

Your answer:

Screen shot 2016 01 12 at 3.00.23 pm

Your answer:

Screen shot 2016 01 13 at 9.26.03 am

Your answer:

Screen shot 2016 01 13 at 9.25.36 am

Your answer:

Screen shot 2016 01 13 at 9.26.38 am

Correct answer:

Screen shot 2016 01 23 at 8.33.58 am

Explanation:

This question tests one's ability to graph a square root function.

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: Make a table of (x,y) coordinates for the function.

$\begin{tabular}{ |c|c|c|c| } \hline x & f(x) & y \\ \hline 2& f(2) & 0 \\ -2 & f(-2) & 2 \\ -7&f(-7)& 3\\ \hline \end{tabular}$

The values in the table are found by substituting in the x values into the function as follows.

$\\f(2)=\sqrt{-2+2}=\sqrt{0}=0 \\f(-2)=\sqrt{--2+2}=\sqrt{4}=2 \\f(-7)=\sqrt{--7+2}=\sqrt{9}=3$

Step 2: Plot the points on a coordinate grid

Screen shot 2016 01 23 at 8.48.27 am

Step 3: Connect the points with a smooth curve.

Recall that a square root function cannot have negative values under the radical therefore, no x values more than two will be in the domain.

Screen shot 2016 01 23 at 8.33.58 am

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All Common Core: High School - Functions Resources

Flashcards: Graph Square Root, Cube Root, and Piecewise Functions: CCSS.Math.Content.HSF-IF.C.7b

Flashcards: Graph Square Root, Cube Root, and Piecewise Functions: CCSS.Math.Content.HSF-IF.C.7b

Flashcards: Graph Square Root, Cube Root, and Piecewise Functions: CCSS.Math.Content.HSF-IF.C.7b

Flashcards: Graph Square Root, Cube Root, and Piecewise Functions: CCSS.Math.Content.HSF-IF.C.7b

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