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 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 the absolute value have on the graph?

Back

A negative sign in front of the absolute value, such as in y = -|x|, reflects the graph across the x-axis.

Front

What is the transformation for the equation y = |x - 3|?

Back

The equation y = |x - 3| represents a horizontal shift of the graph of y = |x| to the right by 3 units.

Front

What is the transformation for the equation y = |x| + 2?

Back

The equation y = |x| + 2 represents a vertical shift of the graph of y = |x| upwards by 2 units.

Front

What is the vertex of the function y = |x - 2| + 3?

Back

The vertex of the function y = |x - 2| + 3 is at the point (2, 3).

Front

What does a vertical stretch of the absolute value function look like?

Back

A vertical stretch occurs when the function is multiplied by a factor greater than 1, such as in y = 3|x|, making the V-shape narrower.

Front

What is the transformation for the equation y = -2|x|?

Back

The equation y = -2|x| represents a vertical stretch by a factor of 2 and a reflection across the x-axis.

Front

How does the equation y = |x + 1| - 4 transform the graph of y = |x|?

Back

The equation y = |x + 1| - 4 shifts the graph left by 1 unit and down by 4 units.

Front

What is the effect of a compression on the absolute value function?

Back

A compression occurs when the function is multiplied by a factor between 0 and 1, such as in y = 0.5|x|, making the V-shape wider.