Graphing Absolute Value Functions

Front

What is an absolute value function?

Back

An absolute value function is a function that outputs the distance of a number from zero on the number line, regardless of direction. It is defined as f(x) = |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 equation y = |x - 3| transform the graph of y = |x|?

Back

The equation y = |x - 3| shifts the graph of y = |x| to the right by 3 units.

Front

What is the effect of adding a constant outside the absolute value, like in y = |x| + 3?

Back

Adding a constant outside the absolute value shifts the graph vertically. In this case, y = |x| + 3 shifts the graph up by 3 units.

Front

What is the domain of the absolute value function?

Back

The domain of the absolute value function is all real numbers, denoted as (-∞, ∞).

Front

What is the range of the absolute value function?

Back

The range of the absolute value function is all non-negative real numbers, denoted as [0, ∞).

Front

How does the equation y = |x + 5| transform the graph of y = |x|?

Back

The equation y = |x + 5| shifts the graph of y = |x| to the left by 5 units.

Front

What does the equation y = |x| - 2 represent?

Back

The equation y = |x| - 2 shifts the graph of y = |x| down by 2 units.

Front

What is the vertex of the graph of y = |x - 5|?

Back

The vertex of the graph of y = |x - 5| is at the point (5, 0).

Front

How do you identify the vertex of an absolute value function in the form y = |x - h|?

Back

In the form y = |x - h|, the vertex is at the point (h, 0).