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Algebra II : Functions and Graphs

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #31 : Transformations Of Linear Functions

Shift the graph 2x+3y = 6 down six units. What is the new equation?

Possible Answers:

$y=-\frac{2}{3}x$

$y=-\frac{2}{3}x-16$

$y=-\frac{2}{3}x-4$

$y=-\frac{2}{3}x+6$

$y=-\frac{2}{3}x-8$

Correct answer:

$y=-\frac{2}{3}x-4$

Explanation:

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

y=mx+b

Subtract from both sides.

2x+3y -2x= 6-2x

3y=-2x+6

Divide by three on both sides.

$\frac{3y}{3}=\frac{-2x+6}{3}$

Simplify this equation.

$y=-\frac{2}{3}x+2$

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

$y=-\frac{2}{3}x+2-6$

The answer is: $y=-\frac{2}{3}x-4$

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Example Question #82 : Linear Functions

Translate the graph y=10-2x down fifteen units. What is the new equation?

Possible Answers:

y=-2x-5

y=-13x+10

y=-2x-25

y=-2x+25

y=-2x+5

Correct answer:

y=-2x-5

Explanation:

The given equation can be rewritten in slope-intercept format, y=mx+b .

$y=10-2x \rightarrow y=-2x+10$

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

y=-2x+10-15

The answer is: y=-2x-5

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Example Question #83 : Linear Functions

Translate the graph y=2x+5 left four units and up one unit. What's the new equation?

Possible Answers:

y= 2x-17

y= 2x-3

y= 2x-7

y= 2x+14

y= 2x+8

Correct answer:

y= 2x+14

Explanation:

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

y=2x+5+(1) = 2x+6

If the graph is to be shifted four units to the left, the x-variable will need to be replaced with the quantity (x+4) .

y=2(x+4)+6

Use the distribution property to simplify the binomial.

y=2x+8+6 = 2x+14

The equation is: y= 2x+14

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Example Question #84 : Linear Functions

Shift the function x+3y=6 up four units. What is the new equation?

Possible Answers:

$y=-\frac{1}{3}x+6$

$y=-\frac{1}{3}x+\frac{16}{3}$

$y=-3x+\frac{16}{3}$

$y=-\frac{1}{3}x+\frac{3}{10}$

y=-3x+6

Correct answer:

$y=-\frac{1}{3}x+6$

Explanation:

Rewrite this equation in standard form to slope intercept format.

Subtract on both sides.

x+3y-x=6-x

3y=-x+6

Divide by three on both sides.

$\frac{3y}{3}=\frac{-x+6}{3}$

Simplify this equation.

$y=-\frac{1}{3}x+2$

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

$y=-\frac{1}{3}x+2+4$

The answer is: $y=-\frac{1}{3}x+6$

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Example Question #85 : Linear Functions

Shift y=6x-4 left eight units. What is the new equation?

Possible Answers:

y= 6x-52

y= 6x+12

y= 6x+44

y= -2x+44

y= 6x-36

Correct answer:

y= 6x+44

Explanation:

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

Replace the term and simplify the equation.

y=6(x+8)-4

Distribute the six through the binomial.

y=6x+48-4 = 6x+44

The equation is: y= 6x+44

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Example Question #86 : Linear Functions

Translate the function y=3-9x left 5 units. What is the new equation?

Possible Answers:

y=-9x+46

y=-9x-42

y=-9x-15

y=-9x-62

y=-9x+18

Correct answer:

y=-9x-42

Explanation:

If the graph is shifted leftward, apply the transformation by replacing the x-variable with (x+5) .

y=3-9(x+5)

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

y=3-9x-45

Combine like-terms.

The answer is: y=-9x-42

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Example Question #87 : Linear Functions

Translate the line y= 7-3x down three units and left four units. What is the new equation?

Possible Answers:

y= -3x+8

y= -3x-12

$\textup{The answer is not given.}$

y= -3x-8

y= -3x+16

Correct answer:

y= -3x-8

Explanation:

Rewrite the equation in slope-intercept form: y=mx+b

y=-3x+7

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

y=-3x+7-(3) = -3x+4

y= -3x+4

If the line is shifted left four units, the x-variable will need to be replaced with (x+4) .

y= -3(x+4)+4

Simplify this equation.

y=-3x-12+4 = -3x-8

The answer is: y= -3x-8

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Example Question #88 : Linear Functions

Translate the line x-y=0 left three units and down four units. What is the new equation?

Possible Answers:

y=x+2

y=x-7

y=-x+3

y=-x-6

y=x-1

Correct answer:

y=x-1

Explanation:

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

Add on both sides.

x-y+y=0+y

y=x

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

y=x-4

The line shifted three units to the left means that the x-variable will need to be replaced with (x+3) .

Rewrite the equation.

y=(x+3)-4

Simplify this equation.

The answer is: y=x-1

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Example Question #371 : Functions And Graphs

Translate the graph y=-3(-x+8) up three units. What is the new equation?

Possible Answers:

y= 3x-24

y= 3x-33

y= 3x-21

y= 3x+15

y= 3x+33

Correct answer:

y= 3x-21

Explanation:

Simplify the equation by distribution.

y=-3(-x+8) = (-3)(-x)+(-3)(8) = 3x-24

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

y= 3x-24+3 = 3x-21

The answer is: y= 3x-21

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Example Question #90 : Linear Functions

Shift the graph: y=2(2x+3) up five units. What is the new equation?

Possible Answers:

y =4x+11

y =4x+8

y =4x+10

y =4x+18

y =4x+15

Correct answer:

y =4x+11

Explanation:

Use distribution to simplify this equation. We will need to put the equation in slope-intercept format, y=mx+b

y=2(2x+3) =2(2x)+2(3) =4x+6

The equation becomes: y =4x+6

Shifting this equation up five units will add five to the y-intercept.

The answer is: y =4x+11

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Algebra II : Functions and Graphs

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #31 : Transformations Of Linear Functions

Example Question #82 : Linear Functions

Example Question #83 : Linear Functions

Example Question #84 : Linear Functions

Example Question #85 : Linear Functions

Example Question #86 : Linear Functions

Example Question #87 : Linear Functions

Example Question #88 : Linear Functions

Example Question #371 : Functions And Graphs

Example Question #90 : Linear Functions

All Algebra II Resources

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