Absolute Value Transformations Make-Up

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 does the graph of y = |x| look like?

Back

The graph of y = |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 over the x-axis.

Front

How does the equation y = |x - 1| transform the parent function y = |x|?

Back

The equation y = |x - 1| shifts the graph of y = |x| to the right by 1 unit.

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. For example, y = |x| + 3 shifts the graph up by 3 units.

Front

What does the term 'compression' refer to in absolute value transformations?

Back

Compression refers to making the graph narrower. For example, y = 2|x| compresses the graph of y = |x|.

Front

What does the term 'stretch' refer to in absolute value transformations?

Back

Stretch refers to making the graph wider. For example, y = 0.5|x| stretches the graph of y = |x|.

Front

How do you write an absolute value function that reflects over the x-axis and shifts up 2 units?

Back

The function can be written as y = -|x| + 2.

Front

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

Back

This function reflects the graph of y = |x| over the x-axis and shifts it left by 3 units.

Front

What does the equation y = |x - 4| + 5 represent in terms of transformations?

Back

This equation shifts the graph of y = |x| right by 4 units and up by 5 units.