Algebra II : Functions and Graphs

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #41 : Transformations Of Linear Functions

Shift the graph  three units to the left.  What's the new equation?

Possible Answers:

Correct answer:

Explanation:

In order to shift an equation to the left three units, the x-variable will need to be replaced with the quantity of .  This shifts all points left three units.

Simplify the equation.

The answer is:  

Example Question #42 : Transformations Of Linear Functions

Shift the line  up six units.  What is the new equation?

Possible Answers:

Correct answer:

Explanation:

Add six to the equation since a vertical shift will increase the y-intercept by six units.

Simplify this equation by distribution.

The answer is:  

Example Question #43 : Transformations Of Linear Functions

Translate the function:   to the left 5 units.  What is the equation in slope-intercept format?

Possible Answers:

Correct answer:

Explanation:

Divide by three on both sides.

The equation becomes:  

If this equation shifts to the left five units, we will need to replace the x term with the quantity .

Simplify this equation by distribution.

Combine like-terms.

The answer is:  

Example Question #44 : Transformations Of Linear Functions

Translate the function  to the left four units.  What is the new equation?

Possible Answers:

Correct answer:

Explanation:

Translation of a graph to the left four units will require replacing the x-variable with the quantity:

Replace the term inside the equation.

Use distribution so simplify the terms.

Simplify the equation.

The answer is:  

Example Question #45 : Transformations Of Linear Functions

Shift the equation  up two units.   What is the new equation?

Possible Answers:

Correct answer:

Explanation:

In order to find the equation after the translation, we will need to put the equation in slope-intercept format, .

Subtract  from both sides of the equation.

The equation becomes:  

Divide by three on both sides.

Add two to the y-intercept for the vertical shift.  This is the same as adding .

The equation is:  

Example Question #46 : Transformations Of Linear Functions

If the graph  is translated 5 units left, what is the new equation?

Possible Answers:

Correct answer:

Explanation:

Rewrite the given equation in standard form to slope intercept format, .

Subtract x from both sides.

The slope intercept form is:  

If the line is translated 5 units to the left, we need to replace the quantity of x with .

Simplify the equation.  Distribute the negative through the binomial.

The answer is:  

Example Question #47 : Transformations Of Linear Functions

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

Possible Answers:

Correct answer:

Explanation:

Rewrite this equation in slope intercept form .

Add  on both sides.

The equation becomes:

Divide by two on both sides.

The equation in slope intercept form is:  

Shifting this equation down four units means that the y-intercept will be decreased four units.

The answer is:  

Example Question #48 : Transformations Of Linear Functions

Shift the line  left three units.  What is the new equation?

Possible Answers:

Correct answer:

Explanation:

Rewrite the equation  in slope-intercept form:   

Subtract one from both sides.

Divide by three on both sides.

If this line is shifted to the left three units, replace the x-variable with .

Simplify by distribution.

The answer is:  

Example Question #49 : Transformations Of Linear Functions

Shift the equation  to the left two units.  What is the new equation?

Possible Answers:

Correct answer:

Explanation:

If the linear function is shifted left two units, the x-variable must be replaced with the quantity of .

Simplify the equation by distribution.

Combine like terms.

The answer is:  

Example Question #51 : Transformations Of Linear Functions

Translate the equation  left four units.  What is the new equation?

Possible Answers:

Correct answer:

Explanation:

To shift the line left four units, we will need to replace the x-variable with the quantity of:

Replace this term in the original equation.

Use distribution to simplify.

The answer is:  

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