Absolute Value Transformations and Piece-Wise Functions

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 for absolute values?

Back

y = |x|

Front

How does the graph of y = |x| transform when a constant is added outside the absolute value?

Back

The graph shifts vertically. For example, y = |x| + 2 shifts the graph up by 2 units.

Front

What effect does multiplying the absolute value function by a constant have on its graph?

Back

Multiplying by a constant greater than 1 makes the graph skinnier, while multiplying by a constant between 0 and 1 makes it wider.

Front

What is a piecewise function?

Back

A piecewise function is a function that is defined by different expressions for different intervals of the input.

Front

How do you evaluate a piecewise function?

Back

To evaluate a piecewise function, determine which interval the input value falls into and use the corresponding expression.

Front

What is the absolute value equation for the graph that opens upwards and is shifted up by 2 units?

Back

y = |x| + 2

Front

What is the solution set for the equation |x| = 24?

Back

The solution set is {24, -24}.

Front

How do you graph the function y = |x - 3|?

Back

Shift the graph of y = |x| to the right by 3 units.

Front

What is the effect of a negative sign in front of the absolute value function, such as in y = -|x|?

Back

It reflects the graph of y = |x| across the x-axis.