Absolute Value Transformations

Front

What is the definition of absolute value?

Back

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is denoted as |x|.

Front

What is the parent function of absolute value?

Back

The parent function of absolute value is f(x) = |x|.

Front

How does the graph of f(x) = |x| look?

Back

The graph of f(x) = |x| is a V-shaped graph that opens upwards, with its vertex at the origin (0,0).

Front

What effect does a vertical stretch have on the graph of an absolute value function?

Back

A vertical stretch multiplies the output of the function by a factor greater than 1, making the graph narrower.

Front

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

Back

A vertical compression multiplies the output of the function by a factor between 0 and 1, making the graph wider.

Front

What does a horizontal shift to the right mean in the context of absolute value functions?

Back

A horizontal shift to the right means the graph moves to the right by a certain number of units, represented as f(x) = |x - h|.

Front

What does a horizontal shift to the left mean in the context of absolute value functions?

Back

A horizontal shift to the left means the graph moves to the left by a certain number of units, represented as f(x) = |x + h|.

Front

How do you represent a vertical shift upwards in an absolute value function?

Back

A vertical shift upwards is represented by adding a constant to the function, such as f(x) = |x| + k.

Front

How do you represent a vertical shift downwards in an absolute value function?

Back

A vertical shift downwards is represented by subtracting a constant from the function, such as f(x) = |x| - k.

Front

What is the transformation of the function f(x) = |x - 3|?

Back

The function f(x) = |x - 3| represents a horizontal shift to the right by 3 units.