Transformations of Absolute Value Functions

Front

What is the parent function of absolute value?

Back

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

Front

What does a vertical shift of 'k' units do to the graph of f(x) = |x|?

Back

A vertical shift of 'k' units moves the graph up if k is positive and down if k is negative.

Front

How does the graph of f(x) = |x - h| transform the parent function?

Back

The graph shifts horizontally to the right by h units if h is positive and to the left by h units if h is negative.

Front

What effect does a negative sign in front of the absolute value function have?

Back

A negative sign reflects the graph across the x-axis.

Front

What is the vertex of the function f(x) = |x + 3| - 2?

Back

The vertex is (-3, -2).

Front

How do you determine the vertex of an absolute value function in the form f(x) = a|x - h| + k?

Back

The vertex is at the point (h, k).

Front

What transformation does f(x) = |x| + 5 represent?

Back

This represents a vertical shift up by 5 units.

Front

What transformation does f(x) = -|x| + 3 represent?

Back

This represents a reflection across the x-axis and a vertical shift up by 3 units.

Front

If f(x) = |x|, what is the transformation for f(x) = |x - 4|?

Back

This represents a horizontal shift to the right by 4 units.

Front

What is the transformation for f(x) = |x + 2| - 1?

Back

This represents a horizontal shift to the left by 2 units and a vertical shift down by 1 unit.