13. Module A Outcome 3 Solving Absolute Value Eq and Ineq.

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 equation of the form |x| = a?

Back

To solve |x| = a, you set up two equations: x = a and x = -a.

Front

What is the solution set for the equation |3x - 4| = 5?

Back

The solution set is x = 3 and x = -rac{1}{3}.

Front

How do you graph an absolute value function?

Back

An absolute value function, such as f(x) = |x|, forms a V shape on the graph, with the vertex at the origin (0,0).

Front

What is the distance formula between two points (x1, y1) and (x2, y2)?

Back

Front

How do you find the midpoint between two points (x1, y1) and (x2, y2)?

Back

The midpoint M is given by M = (\frac{x1 + x2}{2}, \frac{y1 + y2}{2}).

Front

What does the inequality |x - 2| < 3 represent?

Back

The inequality |x - 2| < 3 represents the interval (2 - 3, 2 + 3) or (-1, 5).

Front

How do you solve the inequality |x + 1| ≥ 4?

Back

To solve |x + 1| ≥ 4, set up two inequalities: x + 1 ≥ 4 and x + 1 ≤ -4, leading to x ≥ 3 or x ≤ -5.

Front

What is the significance of the vertex in an absolute value function?

Back

The vertex of an absolute value function is the point where the graph changes direction, representing the minimum or maximum value.

Front

How do you determine the intervals where an absolute value function is greater than a constant?

Back

To determine intervals where |f(x)| > k, solve the inequalities f(x) > k and f(x) < -k.