GRAPHING ABSOLUTE VALUE FUNCTIONS

Front

What is an absolute value function?

Back

An absolute value function is a function that contains an algebraic expression within absolute value symbols, which measures the distance of a number from zero on the number line, resulting in a non-negative output.

Front

How does horizontal translation affect the graph of an absolute value function?

Back

Horizontal translation shifts the graph left or right. For example, f(x) = |x - h| translates the graph h units to the right.

Front

What is the effect of a vertical stretch on the graph of an absolute value function?

Back

A vertical stretch occurs when the output of the function is multiplied by a factor greater than 1. For example, f(x) = a|x| (where a > 1) stretches the graph vertically.

Front

What does the negative sign in front of an absolute value function indicate?

Back

The negative sign reflects the graph of the function across the x-axis.

Front

What is the vertex of the absolute value function f(x) = |x - 3| + 2?

Back

The vertex is the point (3, 2), which is the minimum point of the graph.

Front

How do you determine the domain of an absolute value function?

Back

The domain of an absolute value function is all real numbers, as there are no restrictions on the input values.

Front

What is the range of the function f(x) = |x|?

Back

The range of f(x) = |x| is [0, ∞), as the output is always non-negative.

Front

What is the effect of adding a constant outside the absolute value function?

Back

Adding a constant outside the absolute value function shifts the graph vertically. For example, f(x) = |x| + k shifts the graph up by k units.

Front

How do you graph the function f(x) = -|x + 1| + 3?

Back

Start with the graph of f(x) = |x + 1|, reflect it across the x-axis, and then shift it up 3 units.

Front

What is the significance of the coefficient in front of the absolute value in f(x) = a|x|?

Back

The coefficient 'a' affects the steepness of the graph. If |a| > 1, the graph is steeper; if 0 < |a| < 1, the graph is wider.