Algebra II : Transformations of Linear Functions

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #31 : Transformations Of Linear Functions

Shift the equation  up three units and left six units.  What is the new equation?

Possible Answers:

Correct answer:

Explanation:

Rewrite the equation in slope intercept form.

Shifting the graph up by three units will require adding three to the y-intercept.

Shifting the graph left six units mean that the x-variable will need to be replaced with:  

The equation becomes:

Simplify this equation.

The answer is:  

Example Question #31 : Transformations Of Linear Functions

Shift the graph  down six units.  What is the new equation?

Possible Answers:

Correct answer:

Explanation:

Rewrite the given equation in standard form to slope-intercept form.

Subtract  from both sides.

Divide by three on both sides.

Simplify this equation.

Shifting this equation down means that the y-intercept will be subtracted six.

The answer is:  

Example Question #82 : Linear Functions

Translate the graph  down fifteen units.  What is the new equation?

Possible Answers:

Correct answer:

Explanation:

The given equation can be rewritten in slope-intercept format, .

Shifting down a line fifteen units will decrease the y-intercept by 15.

The answer is:  

Example Question #83 : Linear Functions

Translate the graph  left four units and up one unit.  What's the new equation?

Possible Answers:

Correct answer:

Explanation:

Shifting the equation up one unit will change the y-intercept by adding one.

If the graph is to be shifted four units to the left, the x-variable will need to be replaced with the quantity .

Use the distribution property to simplify the binomial.

The equation is:  

Example Question #84 : Linear Functions

Shift the function  up four units.  What is the new equation?

Possible Answers:

Correct answer:

Explanation:

Rewrite this equation in standard form to slope intercept format.

Subtract  on both sides.

Divide by three on both sides.

Simplify this equation.

If this graph is shifted up four units, simply add four to the y-intercept.

The answer is: 

Example Question #85 : Linear Functions

Shift  left eight units.  What is the new equation?

Possible Answers:

Correct answer:

Explanation:

Shifting the graph left 8 units will require changing the x-variable to .

Replace the term and simplify the equation.

Distribute the six through the binomial.

The equation is:  

Example Question #86 : Linear Functions

Translate the function  left 5 units.  What is the new equation?

Possible Answers:

Correct answer:

Explanation:

If the graph is shifted leftward, apply the transformation by replacing the x-variable with .

Simplify this equation by distribution, and rewrite this in slope intercept format.

Combine like-terms.

The answer is:  

Example Question #87 : Linear Functions

Translate the line  down three units and left four units.  What is the new equation?

Possible Answers:

Correct answer:

Explanation:

Rewrite the equation in slope-intercept form:  

Shifting this line down three units will decrease the y-intercept by three.

If the line is shifted left four units, the x-variable will need to be replaced with .

Simplify this equation.

The answer is:  

Example Question #88 : Linear Functions

Translate the line  left three units and down four units.  What is the new equation?

Possible Answers:

Correct answer:

Explanation:

Rewrite the given equation in standard form to slope-intercept form.

Add  on both sides.

A shift down four units will decrease the y-intercept by four.  The current y-intercept is zero.  Rewrite the equation.

The line shifted three units to the left means that the x-variable will need to be replaced with .

Rewrite the equation.

Simplify this equation.

The answer is:  

Example Question #371 : Functions And Graphs

Translate the graph  up three units.  What is the new equation?

Possible Answers:

Correct answer:

Explanation:

Simplify the equation by distribution.

Shifting this line up by three units will add three to the y-intercept.

The answer is:  

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