Absolute Value Functions

Front

What is the definition of an absolute value function?

Back

An absolute value function is a function that contains an absolute value expression, typically in the form f(x) = |x|, which measures the distance of x from zero on the number line.

Front

What does the graph of an absolute value function look like?

Back

The graph of an absolute value function is a V-shaped graph that opens upwards, with the vertex at the point where the expression inside the absolute value equals zero.

Front

How does the coefficient in front of the absolute value affect the graph?

Back

A coefficient greater than 1 makes the graph narrower, while a coefficient between 0 and 1 makes it wider.

Front

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

Back

The vertex is the point (h, k) where the graph changes direction.

Front

What does the transformation |x - h| represent in the function f(x) = a|x - h| + k?

Back

It represents a horizontal shift to the right by h units.

Front

What does the transformation |x| + k represent in the function f(x) = a|x| + k?

Back

It represents a vertical shift upward by k units.

Front

How do you determine if a relation is a function?

Back

A relation is a function if each input (x-value) has exactly one output (y-value).

Front

Evaluate f(x) = 3|x - 2| for f(4).

Back

f(4) = 3|4 - 2| = 3(2) = 6.

Front

What is the effect of a negative coefficient in front of the absolute value function?

Back

A negative coefficient reflects the graph across the x-axis.

Front

What is the equation of the absolute value function that has a vertex at (3, -2)?

Back

f(x) = |x - 3| - 2.