Absolute Value Functions and Inequalities

Front

What is the definition of 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, denoted as f(x) = |x|.

Front

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

Back

The vertex is the point (3, 2).

Front

How does the graph of f(x) = |x| shift if we change it to f(x) = |x + 2|?

Back

The graph shifts 2 units to the left.

Front

What is the effect of a negative sign in front of an absolute value function, such as f(x) = -|x|?

Back

It reflects the graph across the x-axis.

Front

What does the inequality y < |x| represent on a graph?

Back

It represents the region below the V-shaped graph of y = |x|.

Front

How do you solve the inequality |x - 4| < 3?

Back

You solve it by breaking it into two inequalities: -3 < x - 4 < 3, which simplifies to 1 < x < 7.

Front

What is the equation of the absolute value function that has a vertex at (0, 4)?

Back

The equation is f(x) = |x| + 4.

Front

What does the notation |x| ≤ 5 represent?

Back

It represents all x values that are within 5 units from 0, or -5 ≤ x ≤ 5.

Front

What is the solution set for the inequality |x + 1| > 2?

Back

The solution set is x < -3 or x > 1.

Front

What transformation occurs in the function f(x) = |x| - 5?

Back

The graph shifts down 5 units.