Absolute Value Functions Review

Front

What is the definition of an absolute value function?

Back

An absolute value function is a function that outputs the distance of a number from zero on the number line, denoted as f(x) = |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 negative sign in front of an absolute value function have?

Back

A negative sign in front of an absolute value function reflects the graph across the x-axis.

Front

What does the equation f(x) = |x - 4| represent?

Back

The equation f(x) = |x - 4| represents a rightward shift of the parent function f(x) = |x| by 4 units.

Front

What transformation does the equation y = |x| + 3 represent?

Back

The equation y = |x| + 3 represents a vertical shift of the graph of the parent function up by 3 units.

Front

What does the equation y = -|x| - 2 represent?

Back

The equation y = -|x| - 2 represents a reflection across the x-axis and a downward shift by 2 units.

Front

How do you write the equation for a vertical compression of an absolute value function?

Back

To write the equation for a vertical compression, multiply the absolute value function by a factor less than 1, e.g., y = (2/5)|x|.

Front

What does the transformation y = |x + 3| indicate?

Back

The transformation y = |x + 3| indicates a leftward shift of the graph by 3 units.

Front

What is the effect of adding a constant outside the absolute value function?

Back

Adding a constant outside the absolute value function shifts the graph vertically.