Absolute Value Equations/Inequalities

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 written as |x| = a, where a is a non-negative number.

Front

What are the possible solutions for the equation |x| = a?

Back

The solutions are x = a and x = -a.

Front

What is the graph of the absolute value function y = |x|?

Back

The graph is a V-shaped graph that opens upwards, with the vertex at the origin (0,0).

Front

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

Back

Split into two cases: x - 3 = 5 and x - 3 = -5. Solutions are x = 8 and x = -2.

Front

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

Back

The range is [0, infinity) because absolute values cannot be negative.

Front

What is the domain of the absolute value function?

Back

The domain of the absolute value function is (-infinity, infinity).

Front

How do you graph the function f(x) = |x - 2| + 3?

Back

Shift the graph of y = |x| to the right by 2 units and up by 3 units.

Front

What is the effect of a negative coefficient in front of an absolute value function, such as y = -|x|?

Back

It reflects the graph across the x-axis, making it open downwards.

Front

What is the solution set for the inequality |x| < 4?

Back

The solution set is (-4, 4).