Graphing Absolute Value Functions

Front

What is the general form of an absolute value function?

Back

The general form is y = |x - h| + k, where (h, k) is the vertex of the graph.

Front

What does the expression |x| represent?

Back

The expression |x| represents the distance of x from 0 on the number line, always yielding a non-negative value.

Front

How does the graph of y = |x| differ from y = |x - 3|?

Back

The graph of y = |x - 3| is shifted 3 units to the right compared to y = |x|.

Front

What transformation does y = |x| + 4 represent?

Back

This represents a vertical shift of the graph of y = |x| upwards by 4 units.

Front

What transformation does y = |x + 2| represent?

Back

This represents a horizontal shift of the graph of y = |x| to the left by 2 units.

Front

What is the vertex of the function y = |x - 1| + 2?

Back

The vertex is at the point (1, 2).

Front

How do you find the y-intercept of the function y = |x + 3| - 4?

Back

To find the y-intercept, set x = 0: y = |0 + 3| - 4 = 3 - 4 = -1, so the y-intercept is (0, -1).

Front

What does the transformation 'right 3, up 2' mean for the function y = |x|?

Back

It means the graph of y = |x| is shifted 3 units to the right and 2 units up, resulting in y = |x - 3| + 2.

Front

Evaluate |–3|.

Back

|–3| = 3.

Front

What is the effect of a negative sign in front of the absolute value, such as in -|x|?

Back

It reflects the graph of y = |x| across the x-axis.