Unit 3 Absolute Value Retest

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

What is the general form of an absolute value equation?

Back

An absolute value equation is typically in the form |A| = B, where A is an expression and B is a non-negative number.

Front

How do you solve the equation |x - 3| = 5?

Back

To solve |x - 3| = 5, set up two equations: x - 3 = 5 and x - 3 = -5. The solutions are x = 8 and x = -2.

Front

What is the sum of the solutions to the equation 2 |x - 4| + 8 = 18?

Back

The sum of the solutions is 8.

Front

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

Back

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

Front

What is the domain of all absolute value functions?

Back

The domain of all absolute value functions is (-∞, ∞).

Front

How do you express the solution to the inequality |7x + 4| ≥ 74?

Back

To solve |7x + 4| ≥ 74, set up two inequalities: 7x + 4 ≥ 74 and 7x + 4 ≤ -74.

Front

What is the proper inequality solution for the graph showing x ≤ -7 or x ≥ 3?

Back

The solution is x ≤ -7 or x ≥ 3.

Front

What is the proper inequality solution for the graph showing -4 < x < 2?

Back

The solution is -4 < x < 2.

Front

What is the difference between strict and non-strict inequalities?

Back

Strict inequalities (<, >) do not include the endpoints, while non-strict inequalities (≤, ≥) do include the endpoints.