Absolute Value Transformations

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 transformation y = a|x| represent when a > 1?

Back

It represents a vertical stretch of the graph of y = |x| by a factor of a.

Front

What does the transformation y = a|x| represent when 0 < a < 1?

Back

It represents a vertical compression of the graph of y = |x| by a factor of a.

Front

How does the graph of y = |x - h| shift?

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 adding a constant k to the equation y = |x| have?

Back

Adding a constant k shifts the graph vertically; it shifts up if k is positive and down if k is negative.

Front

What is the vertex of the function y = a|x - h| + k?

Back

The vertex is the point (h, k) on the graph.

Front

What transformation occurs in the equation y = -|x|?

Back

This represents a reflection of the graph of y = |x| across the x-axis.

Front

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

Back

This shifts the graph of y = |x| up by 3 units.

Front

What is the effect of the transformation y = |x + 2|?

Back

This shifts the graph of y = |x| left by 2 units.

Front

What is the transformation for the equation y = 5|x|?

Back

Vertical Stretch.