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All Common Core: High School - Functions Resources

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

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Flashcards: Common Core: High School - Functions

Graph the function and identify the roots.

2x^2-4

Question8

$\text{Roots: }x=\pm\sqrt{2}$

Question7

$\text{Roots: }x=\pm1$

Question9

$\text{Roots: }x=\pm\sqrt{2}$

Question3

$\text{Roots: }x=\pm3$

Question4

$\text{Roots: }x=\pm3$

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Flashcards: Common Core: High School - Functions

Graph the function and identify the roots.

2x^2-4

Your answer:

Question8

$\text{Roots: }x=\pm\sqrt{2}$

Your answer:

Question7

$\text{Roots: }x=\pm1$

Your answer:

Question3

$\text{Roots: }x=\pm3$

Your answer:

Question4

$\text{Roots: }x=\pm3$

Correct answer:

Question9

$\text{Roots: }x=\pm\sqrt{2}$

Explanation:

his question tests one's ability to graph a polynomial function.

For the purpose of Common Core Standards, "graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior" 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: Use algebraic techniques to solve for the roots.

$\\2x^2-4=0 \\2x^2=4 \\x^2=2 \\x=\pm\sqrt{2}$

Step 2: Create a table of (x,y) pairs.

$\begin{tabular}{ |c|c|c|c|c|c|c| } \hline x & f(x) & y \\ \hline -2& f(-2) & 4 \\ -1&f(-1)& -2\\ 0&f(0)&-4\\ \hline \end{tabular}$

Step 3: The values in the table are found by substituting in the x values into the function as follows.

$\\f(-2)=2(-2)^2-4=2(4)-4=8-4=4 \\f(-1)=2(-1)^2-4=2(1)-4=2-4=-2 \\f(0)=2(0)^2-4=0-4=-4$

Step 4: Plot the points on a coordinate grid and connect them with a smooth curve.

Question9

Flashcards: Common Core: High School - Functions

Which graph represents the the inverse of the following function?

Y x 2

Y x 4

Y x 2

Y 2x

Screen shot 2016 01 19 at 11.41.22 am

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Flashcards: Common Core: High School - Functions

Which graph represents the the inverse of the following function?

Y x 2

Your answer:

Y x 2

Your answer:

Y x 4

Your answer:

Y x 2

Your answer:

Screen shot 2016 01 19 at 11.41.22 am

Correct answer:

Y 2x

Explanation:

This question is testing ones ability to recognize and construct a function's inverse from its graph.

For the purpose of Common Core Standards, "Read values of an inverse function from a graph or a table, given that the function has an inverse." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.4c). It is important to note that this standard is not directly tested on but is used for building a deeper understanding on inverses and their functions.

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 it means to be an inverse.

An inverse function is found algebraically as follows.

$y=x+c\Rightarrow x=y+c$

Now solve for the variable in the new (inverse) function.

$\\x=y+c \\x-c=y \\y^{-1}=x-c$

Graphically, the inverse is the mirror image reflected over the line of symmetry. In other words, the coordinate pair components are switched.

Y x 2

Step 2: Construct coordinate pairs of the given graph.

Looking at the graph above, the following table of coordinate pairs can be constructed.

$\begin{tabular}{ |c|c| } \hline x & y \\ \hline 0 & 0 \\ 2&1\\ 4&2\\ 6&3\\ 8& 4 \\ \hline \end{tabular}$

Step 3: Swap the points with the points to create the coordinate pairs of the inverse graph.

$\begin{tabular}{ |c|c| } \hline x & y \\ \hline 0&0 \\ 1&2\\ 2&4\\ 3&6\\4&8 \\ \hline \end{tabular}$

Step 4: Graph the inverse function.

Y 2x

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All Common Core: High School - Functions Resources

Flashcards: Common Core: High School - Functions

Flashcards: Common Core: High School - Functions

Flashcards: Common Core: High School - Functions

Flashcards: Common Core: High School - Functions

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