Absolute Value Graphing

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

How does the graph of y = |x - h| + k transform the parent function y = |x|?

Back

The graph shifts right by h units and up by k units.

Front

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

Back

The vertex is the point (h, k).

Front

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

Back

If |a| > 1, the graph is narrower than the parent function; if 0 < |a| < 1, it is wider.

Front

What is the equation of the absolute value function with vertex (0, 4)?

Back

The equation is y = |x| + 4.

Front

How do you determine if a graph is narrow, wide, or the same compared to the parent function?

Back

Compare the coefficient 'a' in y = a|x|: |a| > 1 is narrow, |a| < 1 is wide, and |a| = 1 is the same.

Front

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

Back

The graph shifts up 3 units.

Front

What is the transformation of the graph y = -|x|?

Back

The graph reflects over the x-axis.

Front

What is the equation of the graph that has a vertex at (1, -2) and opens upwards?

Back

The equation is y = |x - 1| - 2.