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Common Core: High School - Functions : Construct Linear and Exponential Functions, Arithmetic and Geometric Sequences: CCSS.Math.Content.HSF-LE.A.2

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All Common Core: High School - Functions Resources

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Example Questions

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Example Question #41 : Linear, Quadratic, & Exponential Models*

What is the function that describes the graph?

Q11

Possible Answers:

$y=\frac{1}{2}x-2$

$y=\frac{3}{4}x$

$y=\frac{3}{4}x-1$

$y=\frac{1}{2}x+1$

$y=\frac{4}{3}x$

Correct answer:

$y=\frac{3}{4}x$

Explanation:

This question is testing one's ability to identify and construct an algebraic function given a graph.

For the purpose of Common Core Standards, "Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table)." falls within the Cluster A of "Construct and compare linear, quadratic, and exponential models and solve problems" concept (CCSS.MATH.CONTENT.HSF-LE.A.2).

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 -intercept.

Recall that the -intercept is the point at which the line crosses the -axis. In other words, it is at the point where x=0 .

Q11

$\textup{y-intercept}=0$

Step 2: Identify the slope.

Recall that slope is known as rise over run or the change in the y values over the change in x values.

$\frac{\textup{rise}}{\textup{run}}=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}$

The rise is three units up and the run is four units to the right.

$\textup{slope}=\frac{\textup{rise}}{\textup{run}}=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}=\frac{3-1}{4-0}=\frac{3}{4}$

Step 3: Construct the equation using the slope-intercept form of a linear function.

The slope-intercept form of a linear function is,

$\\y=mx+b \\m=\textup{Slope} \\b=\textup{y-intercept}$ .

Substitute the slope and intercept into the general form to construct this particular function.

$y=\frac{3}{4}x$

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Example Question #42 : Linear, Quadratic, & Exponential Models*

What is the function that describes the graph?

Q12

Possible Answers:

y=-x+2

y=-x-2

y=-x

y=x+2

y=x-2

Correct answer:

y=-x+2

Explanation:

This question is testing one's ability to identify and construct an algebraic function given a graph.

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 -intercept.

Recall that the -intercept is the point at which the line crosses the -axis. In other words, it is at the point where x=0 .

Q12

$\textup{y-intercept}=2$

Step 2: Identify the slope.

Recall that slope is known as rise over run or the change in the y values over the change in x values.

$\frac{\textup{rise}}{\textup{run}}=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}$

The rise is one unit down and the run is one unit to the right.

$\textup{slope}=\frac{\textup{rise}}{\textup{run}}=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}=\frac{1-2}{1-0}=\frac{-1}{1}=-1$

Step 3: Construct the equation using the slope-intercept form of a linear function.

The slope-intercept form of a linear function is,

$\\y=mx+b \\m=\textup{Slope} \\b=\textup{y-intercept}$ .

Substitute the slope and intercept into the general form to construct this particular function.

y=-x+2

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All Common Core: High School - Functions Resources

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Common Core: High School - Functions : Construct Linear and Exponential Functions, Arithmetic and Geometric Sequences: CCSS.Math.Content.HSF-LE.A.2

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

All Common Core: High School - Functions Resources

Example Questions

Example Question #41 : Linear, Quadratic, & Exponential Models*

Example Question #42 : Linear, Quadratic, & Exponential Models*

All Common Core: High School - Functions Resources

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