Absolute Value Transformations Review

Front

What is the parent function of absolute value?

Back

y = |x|

Front

What does it mean to reflect a function over the x-axis?

Back

The output values of the function are multiplied by -1, flipping the graph upside down.

Front

How does a vertical stretch affect the graph of an absolute value function?

Back

It makes the graph narrower; for example, y = k|x| (k > 1) is skinnier than y = |x|.

Front

What is the effect of a vertical compression on the graph of an absolute value function?

Back

It makes the graph wider; for example, y = k|x| (0 < k < 1) is wider than y = |x|.

Front

What does a horizontal shift to the right by 3 units look like in an absolute value function?

Back

y = |x - 3|.

Front

What does a vertical shift up by 4 units look like in an absolute value function?

Back

y = |x| + 4.

Front

What is the vertex of the function y = |x - 2| + 3?

Back

(2, 3)

Front

How do you write an absolute value function that is reflected over the x-axis?

Back

Use a negative sign in front of the absolute value, e.g., y = -|x|.

Front

What is the range of the absolute value function y = |x|?

Back

[0, infinity) because the output is always non-negative.

Front

What transformation does the equation y = -|x + 1| - 5 represent?

Back

Reflection over the x-axis, left 1 unit, and down 5 units.