Transformations of Absolute Value Functions

Front

What is the parent function of absolute value?

Back

y = |x|

Front

What does a positive 'a' value in y = a|x| indicate?

Back

The graph opens upwards.

Front

What does a negative 'a' value in y = a|x| indicate?

Back

The graph opens downwards.

Front

What effect does a value greater than 1 for 'a' have on the graph of y = a|x|?

Back

It stretches the graph vertically.

Front

What effect does a value between 0 and 1 for 'a' have on the graph of y = a|x|?

Back

It compresses the graph vertically.

Front

What does the term 'horizontal translation' refer to in transformations?

Back

Shifting the graph left or right along the x-axis.

Front

What does the term 'vertical translation' refer to in transformations?

Back

Shifting the graph up or down along the y-axis.

Front

How does the equation y = |x - h| represent a horizontal shift?

Back

It shifts the graph h units to the right if h is positive and left if h is negative.

Front

How does the equation y = |x| + k represent a vertical shift?

Back

It shifts the graph k units up if k is positive and down if k is negative.

Front

What does the transformation y = -|x| represent?

Back

A reflection of the graph across the x-axis.