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Algebra II : Functions and Graphs

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Example Questions

Example Question #11 : Transformations Of Linear Functions

Suppose 2x+2y=3 is shifted left two units. What is the new equation in slope-intercept form?

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

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

Subtract from both sides.

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

2y=-2x+3

Divide by two on both sides.

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

Simplify both sides.

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

If this equation is shifted left two units, the will be replaced with x+2 .

Rewrite the equation and simplify.

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

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

The answer is: $y=-x-\frac{1}{2}$

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Example Question #12 : Transformations Of Linear Functions

Shift y=2(x+3)-3 left four units. Write the new equation.

Possible Answers:

y=2x+8

y=2x-6

y=2x+11

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

y=2x-9

Correct answer:

y=2x+11

Explanation:

Simplify the equation given by distributing the integer through the binomial and combine like-terms. This will put the equation in slope intercept form.

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

y=2x+6-3

y=2x+3

Since this equation is shifted left four units, replace with x+4 .

y=2(x+4)+3

Simplify this equation.

y=2x+8+3 = 2x+11

The new equation after the shift is: y=2x+11

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Example Question #61 : Linear Functions

If the line x+2y=3 is shifted up four units, what is the new equation?

Possible Answers:

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

x+2y=7

$y=-\frac{1}{2}x+\frac{7}{2}$

$y=-\frac{1}{2}x+\frac{11}{2}$

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

Correct answer:

$y=-\frac{1}{2}x+\frac{11}{2}$

Explanation:

Rewrite the given equation, x+2y=3 , in standard form to slope intercept form, y=mx+b .

Subtract from both sides.

x+2y-x=-x+3

2y=-x+3

Divide by two on both sides.

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

Simplify the equation.

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

The vertical shift by four units will shift the y-intercept up four units. Add four to the equation.

$y=-\frac{1}{2}x+\frac{3}{2}+(4)=-\frac{1}{2}x+\frac{3}{2}+\frac{8}{2}$

The answer is: $y=-\frac{1}{2}x+\frac{11}{2}$

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Example Question #61 : Linear Functions

Translate the function 2x+2y=1 up two units. What is the y-intercept of the new equation?

Possible Answers:

$1\frac{1}{4}$

$1\frac{1}{2}$

$2\frac{1}{2}$

$\frac{1}{2}$

$2\frac{1}{4}$

Correct answer:

$2\frac{1}{2}$

Explanation:

The equation given is currently in standard form.

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

Subtract on both sides of 2x+2y=1 .

2x+2y-2x=1-2x

2y=-2x+1

Divide by two on both sides.

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

Simplify the fractions and split the right fraction into two parts.

The equation in slope-intercept form is: $y=-x+\frac{1}{2}$

Apply the translation. If this line is shifted up two units, the y-intercept will be added two.

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

The answer is: $2\frac{1}{2}$

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Example Question #65 : Linear Functions

Shift the line x-y = 3 right three units. What is the new equation?

Possible Answers:

y=x

y=x+6

y=x-6

y=3-x

y=3x

Correct answer:

y=x-6

Explanation:

Rewrite the given equation x-y = 3 in standard form to slope-intercept form, y=mx+b .

Add and subtract three on both sides.

x-y +[y]-(3)= 3 +[y]-(3)

Simplify both sides.

y=x-3

Since the line is shifted three units to the right, the term will become x-3 .

Replace this with the variable in the equation.

y=(x-3)-3

Simplify.

The answer is: y=x-6

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Example Question #14 : Transformations Of Linear Functions

Shift the line y=2x-3 up one unit, and left two units. Write the new equation.

Possible Answers:

y=2x+2

y=2x-5

y=2x+4

y=2x-1

y=2x-2

Correct answer:

y=2x+2

Explanation:

Shifting the line up one unit will result in adding one to the y-intercept.

y=2x-3+(1)

y=2x-2

When the line is shifted left two units, the variable must be replaced with the x+2 term.

y=2(x+2)-2

Use the distributive property to expand this equation.

y=2x+4-2 = 2x+2

The new equation is: y=2x+2

The answer is: y=2x+2

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Example Question #67 : Linear Functions

Shift the line y=3x+9 up two units and left three units. What's the new equation?

Possible Answers:

y=3x+11

y=3x+2

y=3x+14

y=3x+8

y=3x+20

Correct answer:

y=3x+20

Explanation:

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

y=3x+9+(2) =3x+11

Shifting the line left three units mean that the x-variable will be replaced with:

x+3

Replace with the quantity of x+3 .

y=3(x+3)+11 = 3x+9+11

Simplify this equation by combining like-terms

The answer is: y=3x+20

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Example Question #15 : Transformations Of Linear Functions

Shift the line y=2(2x-5) left 2 units. Write the new equation.

Possible Answers:

y= 4x+16

y= 4x+8

y= 4x-8

y= 4x-2

y= 4x-16

Correct answer:

y= 4x-2

Explanation:

Expand the equation by distribution.

y=2(2x-5) = 4x-10

Since this line is shifted left two units, replace the variable with x+2 .

The equation becomes:

y=4(x+2)-10 = 4x+8-10 = 4x-2

The new equation after the shift is: y= 4x-2

The answer is: y= 4x-2

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Example Question #11 : Transformations Of Linear Functions

Determine the new equation if y=9x-10 is shifted ten units to the left.

Possible Answers:

y=9x

y=9x-20

y=9x-2

y=9x+70

y=9x+80

Correct answer:

y=9x+80

Explanation:

If a line is shifted ten units to the left, the x-variable will be replaced with (x+10) since the root will be ten units to the left of the original location.

The equation becomes:

y=9(x+10)-10

Simplify the linear equation.

y= 9x+90-10

The answer is: y=9x+80

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Example Question #21 : Transformations Of Linear Functions

Shift the function y=-2x+50 right five units. What's the new equation?

Possible Answers:

y= -2x+45

y= -2x-250

y= -2x+60

y= -2x-60

y= -2x+250

Correct answer:

y= -2x+60

Explanation:

Shifting the line right five units will shift the root right by five units.

This means that the variable will need to be replaced with (x-5) since all of the x-values are shifted right five units.

The new equation becomes: y=-2(x-5)+50

Simplify the equation.

y=-2x+10+50= -2x+60

The answer is: y= -2x+60

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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 #11 : Transformations Of Linear Functions

Example Question #12 : Transformations Of Linear Functions

Example Question #61 : Linear Functions

Example Question #61 : Linear Functions

Example Question #65 : Linear Functions

Example Question #14 : Transformations Of Linear Functions

Example Question #67 : Linear Functions

Example Question #15 : Transformations Of Linear Functions

Example Question #11 : Transformations Of Linear Functions

Example Question #21 : Transformations Of Linear Functions

All Algebra II Resources

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