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 is the parent function of absolute value?

Back

The parent function of absolute value is f(x) = |x|.

Front

How does the graph of y = a|x| differ from the parent function?

Back

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

Front

What effect does adding a constant outside the absolute value have on the graph?

Back

Adding a constant outside the absolute value function shifts the graph vertically. For example, y = |x| + 2 shifts the graph up by 2 units.

Front

What effect does adding a constant inside the absolute value have on the graph?

Back

Adding a constant inside the absolute value function shifts the graph horizontally. For example, y = |x - 3| shifts the graph right by 3 units.

Front

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

Back

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

Front

How do you determine if the graph of y = a|x| is wide, narrow, or the same as the parent function?

Back

Compare the value of 'a': |a| > 1 means narrow, 0 < |a| < 1 means wide, and |a| = 1 means the same.

Front

What is the effect of a negative 'a' in y = a|x|?

Back

A negative 'a' reflects the graph across the x-axis.

Front

What is the equation of the graph that opens downwards?

Back

The equation is of the form y = -a|x - h| + k, where 'a' is positive.

Front

How do you find the x-intercepts of an absolute value function?

Back

Set the absolute value expression equal to zero and solve for x.