Dilations and Translations of Functions

Write an absolute value function, g(x), given the following transformations from the parent function:
--Vertical compression by a factor of 1/9

Write the equation, g(x), for a graph that is vertically compressed by a factor of 2/5 and shifted up 6.

• g(x)=6|x|-2/5

• g(x)=2/5|x|+6

• g(x)=2/5|x+6|

• g(x)=2/5|x-6|

• Horizontal translation 3 units left

• Horizontal translation 3 units right

• Vertical translation 3 units down

• Vertical translation 3 units up

Answer explanation

The + 3 is outside the absolute value bars, so that indicated a VERTICAL change. Because it is after the absolute value, it translates up 3 units.

Tags

2a.6c

• Horizontal translation 45 units left

• Horizontal translation 45 units right

• Vertical translation 45 units down

• Vertical translation 45 units up

Answer explanation

The - 45 is inside the absolute value bars. Since it is after the x, it moves right 45 units.

REMEMBER: Anything horizontal is the opposite of what you might think.

Tags

2a.6c

Where would point J' be if you translated point 5 units to the left and 2 units up?

• (5, 3)

• (3, -5)

• (-5, 3)

• (-3, 5)

How is trapezoid ABCD translated to trapezoid A'B'C'D'?

• Translated 5 units down and 5 units to the right

• Translated 5 units down and 1 to the right

• Translated 8 units down and 5 units to the right

• Translated 5 units down and 4 units to the right

Dilate the figure by a scale factor of 3 with the origin as the center of dilation. What are the coordinates of the image?

• A'(9,9) B'(18,18) C'(27,9)

• A'(6,6) B'(9,9) C'(12,6)

• A'(0,0) B'(3,3) C'(6,0)

• A'(1,1) B'(2,2) C'(3,1)

State the coordinate of the image of the given point B (-10,-6) under a dilation with center at the origin with the given scale factor k = 1/2.

• (5,3)

• (20,12)

• (-20,-12)

• (-5,-3)

State the coordinate of the image of the given point B (4,9) under a dilation with center at the origin with the given scale factor k = 2.

• (2,4.5)

• (-8,-18)

• (8,18)

• (9,4)

Does the image show a Dilation?

• Yes

• No