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SAT II Math II : Transformations

Study concepts, example questions & explanations for SAT II Math II

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All SAT II Math II Resources

2 Diagnostic Tests 130 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Transformations

Axes_1

Refer to the above figure.

Which of the following functions is graphed?

Possible Answers:

g(x) = |x +6| + 3

g(x) = |x+3| + 6

The correct answer is not given among the other responses.

g(x) = |x - 6| + 3

g(x) = |x-3| + 6

Correct answer:

g(x) = |x - 6| + 3

Explanation:

Below is the graph of f(x) = |x| :

Axes_1

The given graph is the graph of shifted 6 units left (that is, unit right) and 3 units up.

The function graphed is therefore

g (x) = f(x-h) + k where h = 6, k= 3 . That is,

g (x) = f(x-6) +3

g(x)= | x-6 | + 3

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Example Question #2 : Coordinate Geometry

Axes_1

Refer to the above figure.

Which of the following functions is graphed?

Possible Answers:

g(x) = |2x + 6|

g(x) = |2x| + 3

$g(x) = \left |3x + \frac{3}{2} \right |\textup{}$

g(x) = |3x +6|

$g(x) =\left | \frac{1}{2} x \right |+ 3$

Correct answer:

g(x) = |2x| + 3

Explanation:

Below is the graph of f(x) = |x| :

Axes_1

If the graph of is translated by shifting each point (x,y) to the point (2, 2y) , the graph of

g(x) = 2f(x)

is formed. If the graph is then shifted upward by three units, the new graph is

g(x) = 2f(x) + 3

Since the starting graph was f(x) = |x| , the final graph is

g(x) = 2 |x| + 3 , or,

g(x) = |2x| + 3

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Example Question #2 : Transformations

Axes_1

Refer to the above figure.

Which of the following functions is graphed?

Possible Answers:

$g(x) =\left | \frac{1}{3} x+\frac{4}{3} \right |$

g(x) =- |3x+12|

g(x) = |3x-12|

$g(x) =\left | \frac{1}{3} x-\frac{4}{3} \right |$

g(x) = |3x+12|

Correct answer:

g(x) = |3x-12|

Explanation:

Below is the graph of f(x) = |x| :

Axes_1

If the graph of is translated by shifting each point (x,y) to the point (x, 3y) , the graph of

g(x) = 3f(x)

is formed. If the graph is then shifted right by four units, the new graph is

g(x) = 3f(x- 4)

Since the starting graph was f(x) = |x| , the final graph is

g(x) = 3 |x-4| , or g(x) = |3x-12|

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Example Question #3 : Transformations

Axes_1

Refer to the above figure.

Which of the following functions is graphed?

Possible Answers:

$g(x) =\left | \frac{1}{4}x-1 \right |$

g(x) =-|4x |- 4

g(x) =-|4x+16|

$g(x) =\left | \frac{1}{4}x+1 \right |$

$g(x) =\left | \frac{1}{4}x \right |- 4$

Correct answer:

$g(x) =\left | \frac{1}{4}x \right |- 4$

Explanation:

Below is the graph of f(x) = |x| :

Axes_1

If the graph of is translated by shifting each point (x,y) to the point $\left ( x, \frac{1}{4}y \right )$ , the graph of

$g(x) = \frac{1}{4}f(x)$

is formed. If the graph is then shifted down by four units, the new graph is

$g(x) = \frac{1}{4}f(x)- 4$ .

Since the starting graph was f(x) = |x| , the final graph is

$g(x) = \frac{1}{4}|x|- 4$ , or

$g(x) =\left | \frac{1}{4}x \right |- 4$

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Example Question #1 : Transformations

Axes_1

Refer to the above figure.

Which of the following functions is graphed?

Possible Answers:

$g(x) =\left | \frac{1}{3} x+ \frac{2}{3} \right |$

g(x) = |3x-6|

$g(x) =\left | \frac{1}{3} x- \frac{2}{3} \right |$

$g(x) =\left | \frac{1}{3} x \right |+2$

g(x) = |3x|-2

Correct answer:

$g(x) =\left | \frac{1}{3} x- \frac{2}{3} \right |$

Explanation:

Below is the graph of f(x) = |x| :

Axes_1

If the graph of is translated by shifting each point (x,y) to the point $\left ( x, \frac{1}{3}y \right )$ , the graph of

$g(x) = \frac{1}{3}f(x)$

is formed. If the graph is then shifted right by two units, the new graph is

$g(x) = \frac{1}{3}f(x-2)$

Since the starting graph was f(x) = |x| , the final graph is

$g(x) = \frac{1}{3} |x-2|$ , or

$g(x) =\left | \frac{1}{3} x- \frac{2}{3} \right |$

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All SAT II Math II Resources

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SAT II Math II : Transformations

Study concepts, example questions & explanations for SAT II Math II

All SAT II Math II Resources

Example Questions

Example Question #1 : Transformations

Example Question #2 : Coordinate Geometry

Example Question #2 : Transformations

Example Question #3 : Transformations

Example Question #1 : Transformations

All SAT II Math II Resources

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