Question 1

What is the transformed equation of the absolute value function

y = |x|

after reflecting it over the x-axis and shifting it 3 units to the right?

Accepted Answer

y = -|x - 3|

Answer

y = -|x - 3|

Answer

y = -|x - 3|

Answer

y = -|x - 3|

Question 2

Which transformation occurs to the absolute value function

y = |x|

if it changes to

y = 2|x + 4| - 5

?

Accepted Answer

The graph is vertically stretched by a factor of 2, shifted left by 4 units, and shifted down by 5 units.

Answer

The graph is vertically stretched by a factor of 2, shifted right by 4 units, and shifted up by 5 units.

Answer

The graph is vertically compressed by a factor of 2, shifted right by 4 units, and shifted up by 5 units.

Answer

The graph is reflected over the x-axis, shifted left by 4 units, and shifted up by 5 units.

Question 3

What is the effect on the graph of the absolute value function

y = |x|

when it is transformed to

y = 2|x + 4| - 5

?

Accepted Answer

The graph is horizontally stretched by a factor of 2 and shifted up by 3 units.

Answer

The graph is horizontally compressed by a factor of 2 and shifted down by 3 units.

Answer

The graph is horizontally compressed by a factor of 0.5 and shifted up by 3 units.

Answer

The graph is vertically stretched by a factor of 2 and shifted up by 3 units.

Question 4

If the absolute value function

y = |x|

is transformed to

y = 2|x + 4| - 5

, what transformations have occurred?

Accepted Answer

The graph is reflected over the x-axis, vertically stretched by a factor of 3, shifted right by 1 unit, and shifted up by 2 units.

Answer

The graph is reflected over the y-axis, compressed vertically by a factor of 3, shifted left by 1 unit, and shifted up by 2 units.

Answer

The graph is reflected over the x-axis, stretched vertically by a factor of 3, shifted left by 1 unit, and shifted down by 2 units.

Answer

The graph is only stretched vertically by a factor of 3 and shifted up by 2 units.

Question 5

How is the graph of the absolute value function

y = |x|

affected when transformed to

y = 2|x + 4| - 5

?

Accepted Answer

The graph is shifted left by 2 units and down by 4 units.

Answer

The graph is shifted right by 2 units and down by 4 units.

Answer

The graph is shifted right by 2 units and up by 4 units.

Answer

The graph is shifted left by 2 units and up by 4 units.

Question 6

What transformation occurs to the absolute value function

y = |x|

when it changes to

y = 2|x + 4| - 5

?

Accepted Answer

The graph is vertically compressed by a factor of 0.5, shifted right by 6 units, and shifted up by 7 units.

Answer

The graph is horizontally compressed by a factor of 0.5, shifted right by 6 units, and shifted up by 7 units.

Answer

The graph is vertically stretched by a factor of 0.5, shifted left by 6 units, and shifted down by 7 units.

Answer

The graph is vertically compressed by a factor of 2, shifted left by 6 units, and shifted down by 7 units.

Question 7

What is the transformation of the absolute value function

y = |x|

to

y = 2|x + 4| - 5

?

Accepted Answer

The graph is reflected over the x-axis, vertically stretched by a factor of 2, shifted left by 5 units, and shifted up by 3 units.

Answer

The graph is only stretched vertically by a factor of 2 and shifted down by 3 units.

Answer

The graph is reflected over the x-axis, compressed vertically by a factor of 2, shifted right by 5 units, and shifted up by 3 units.

Answer

The graph is reflected over the y-axis, compressed vertically by a factor of 2, shifted right by 5 units, and shifted down by 3 units.

Question 8

How is the absolute value function

y = |x|

transformed to

y = 2|x + 4| - 5

?

Accepted Answer

The graph is shifted right by 1 unit and down by 2 units.

Answer

The graph is shifted right by 1 unit and up by 2 units.

Answer

The graph is shifted left by 1 unit and down by 2 units.

Answer

The graph is shifted left by 1 unit and up by 2 units.

Question 9

What is the new equation of the absolute value function

y = |x|

after reflecting it over the y-axis, compressing it vertically by a factor of 2, and shifting it 3 units up?

Accepted Answer

y = -|x - 3|

Answer

y = -|x - 3|

Answer

y = -|x - 3|

Answer

y = -|x - 3|

Question 10

How is the graph of the absolute value function

y = |x|

affected when transformed to

y = 2|x + 4| - 5

?

Accepted Answer

The graph is reflected over the x-axis, vertically compressed by a factor of 0.5, shifted left by 3 units, and shifted down by 4 units.

Answer

The graph is only stretched vertically by a factor of 0.5 and shifted up by 4 units.

Answer

The graph is reflected over the y-axis, vertically stretched by a factor of 2, shifted right by 3 units, and shifted up by 4 units.

Answer

The graph is reflected over the x-axis, compressed vertically by a factor of 2, shifted right by 3 units, and shifted down by 4 units.

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