Review Absolute Value Functions

Front

What is the definition of absolute value?

Back

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is denoted as |x|.

Front

How do you solve an absolute value inequality like |x| < a?

Back

To solve |x| < a, split it into two inequalities: -a < x < a.

Front

What is the solution to the inequality |c + 4| < 5?

Back

-9 < c < 1.

Front

How do you solve an absolute value equation like |x - b| = c?

Back

To solve |x - b| = c, split it into two equations: x - b = c and x - b = -c.

Front

What is the solution to the equation |2x - 3| + 5 = 10?

Back

x = -1 or x = 4.

Front

What does the graph of y = -|x - 2| + 4 look like?

Back

It is a V-shaped graph that opens downwards with a vertex at (2, 4).

Front

What is the solution to the inequality |y - 4| ≥ 8?

Back

y ≤ -4 or y ≥ 12.

Front

How do you interpret the absolute value in real-world contexts?

Back

Absolute value can represent quantities like distance, which cannot be negative.

Front

What is the equation of the graph of an absolute value function?

Back

An absolute value function can be expressed as y = a|x - h| + k, where (h, k) is the vertex.

Front

What is the solution to the equation |6 - 2k| = 18?

Back

k = -6 or k = 12.