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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 #21 : Transformations Of Linear Functions

Shift the line: y=3x-1 up two units and left five units. What is the new equation?

Possible Answers:

y =3x+2

y =3x+6

y =3x-5

y =3x-14

y =3x+16

Correct answer:

y =3x+16

Explanation:

Shifting the line up two units will add two to the y-intercept.

y=3x-1+(2) = 3x+1

Shifting the line left five units will indicate that the x-variable will be changed to:

x+5

Replace this quantity into the equation.

y=3(x+5)+1

Simplify this equation.

y=3x+15+1 =3x+16

The answer is: y =3x+16

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Example Question #22 : Transformations Of Linear Functions

Shift the equation 2x+y=9 left eight units. What's the new equation?

Possible Answers:

y=-2x-50

y=2x-7

y=-2x-25

y=-2x+7

y=-2x-7

Correct answer:

y=-2x-7

Explanation:

If a function is shifted left eight units, we will need to replace the term with the quantity (x+8) .

2(x+8)+y=9

Use the distributive property to simplify the binomial.

2x+16+y=9

Solve for y. Subtract and on both sides.

2x+16+y-[2x]-(16)=9-[2x]-(16)

Simplify both sides.

The answer is: y=-2x-7

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Example Question #23 : Transformations Of Linear Functions

Translate the following function left three units: y=9-6x Write the new equation.

Possible Answers:

y=-6x-9

y=-6x-27

y=-6x+6

y=-6x+27

y=-6x+12

Correct answer:

y=-6x-9

Explanation:

When the graph is shifted three units to the left, the x-variable of the equation will need to be replaced with (x+3) .

Replace the x term with the new term.

y=9-6(x+3)

Simplify this equation.

y=9-6x-18

Combine like-terms.

The answer is: y=-6x-9

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Example Question #884 : Algebra Ii

Translate x+6y=-5 down two units. What's the new equation?

Possible Answers:

$y=-\frac{1}{6}x+\frac{1}{2}$

$y=-\frac{1}{6}x-\frac{17}{6}$

$y=-\frac{1}{6}x+\frac{17}{6}$

$y=-\frac{1}{6}x-\frac{7}{6}$

$y=-\frac{1}{6}x-\frac{1}{2}$

Correct answer:

$y=-\frac{1}{6}x-\frac{17}{6}$

Explanation:

Rewrite the equation, x+6y=-5 , in slope intercept form.

y=mx+b

Subtract on both sides.

x+6y-x=-5-x

6y = -x-5

Divide by six on both sides.

$\frac{6y }{6}= \frac{-x-5}{6}$

Simplify both sides.

The equation in slope intercept form is: $y=-\frac{1}{6}x-\frac{5}{6}$

Shifting the function down by two units mean that the y-intercept will be subtracted by two.

$y=-\frac{1}{6}x-\frac{5}{6}-(2) = -\frac{1}{6}x-\frac{5}{6}-(\frac{12}{6})$

The answer is: $y=-\frac{1}{6}x-\frac{17}{6}$

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Example Question #24 : Transformations Of Linear Functions

Shift the equation y=-5x+6 left five units. What is the new equation?

Possible Answers:

y=-5x+19

y=-5x-19

y=-5x-11

y=-5x+1

y=-5x+35

Correct answer:

y=-5x-19

Explanation:

The graph translated five units to the left will require the x-variable to be replaced with (x+5) .

Replace the term.

y=-5(x+5)+6

Simplify by distribution.

y=-5(x+5)+6 = -5x-25+6

The equation of the new line is: y=-5x-19

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Example Question #76 : Linear Functions

Shift x-y = -1 down four units. Determine the new equation.

Possible Answers:

y=x-4

y=x-3

y=-x+3

y=x+3

y=-x-4

Correct answer:

y=x-3

Explanation:

Convert the equation in standard form to slope-intercept form, y=mx+b .

Add on both sides.

x-y +(y)= -1+(y)

x=y-1

Add one on both sides.

x+1=y-1+1

The equation becomes: x+1=y

Shifting this equation down four units means that the y-intercept must be subtracted four units.

x+1-4=y

The answer is: y=x-3

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Example Question #25 : Transformations Of Linear Functions

Shift y=6x up two units and left two units. What is the new equation?

Possible Answers:

y=6x-14

y=6x+8

y=6x+14

y=6x-4

y=6x-10

Correct answer:

y=6x+14

Explanation:

Apply the vertical transformation. Shifting up two units will add two to the y-intercept.

y=6x+2

Shifting the graph two units to the left will require a replacement of the x-variable with (x+2) .

y=6(x+2)+2

Simplify this equation.

y=6x+12+2= 6x+14

The answer is: y=6x+14

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Example Question #26 : Transformations Of Linear Functions

Shift the equation y=6x-30 right four units. What's the new equation?

Possible Answers:

y=6x+54

y= 6x-26

y= 6x-54

y= 6x+34

y= 6x-41

Correct answer:

y= 6x-54

Explanation:

A translation to the right four units will require the x-variable to be replaced with (x-4) .

Rewrite the equation.

y=6(x-4)-30

Simplify the binomial by distribution.

y=6x-24-30 = 6x-54

The answer is: y= 6x-54

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Example Question #27 : Transformations Of Linear Functions

Shift the equation y= 8x-3 left five units. What is the new equation?

Possible Answers:

y= 8x-16

y= 8x-32

y= 8x+37

y= 8x-37

y= 8x-12

Correct answer:

y= 8x+37

Explanation:

If a linear function is shifted left five units, the x-variable will need to be replaced with (x+5) . Replace the term, and simplify the equation.

y= 8(x+5)-3

Distribute the eight through both terms of the binomial.

y= 8x+40-3 = 8x+37

The answer is: y= 8x+37

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Example Question #31 : Transformations Of Linear Functions

Shift the equation y=9-x up three units and left six units. What is the new equation?

Possible Answers:

y= -x-18

y= -x-6

y= -x+6

y= -x+18

y= -x-12

Correct answer:

y= -x+6

Explanation:

Rewrite the equation in slope intercept form.

y=-x+9

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

y=-x+9=-x+9+(3) = -x+12

Shifting the graph left six units mean that the x-variable will need to be replaced with: (x+6)

The equation becomes:

y=-(x+6)+12

Simplify this equation.

y=-x-6+12 = -x+6

The answer is: y= -x+6

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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 #21 : Transformations Of Linear Functions

Example Question #22 : Transformations Of Linear Functions

Example Question #23 : Transformations Of Linear Functions

Example Question #884 : Algebra Ii

Example Question #24 : Transformations Of Linear Functions

Example Question #76 : Linear Functions

Example Question #25 : Transformations Of Linear Functions

Example Question #26 : Transformations Of Linear Functions

Example Question #27 : Transformations Of Linear Functions

Example Question #31 : Transformations Of Linear Functions

All Algebra II Resources

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