Absolute Value Equations, Inequalities, and Graphing Review

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 solution to the equation |x + 9| = -5?

Back

no solution

Front

Describe the transformation of the equation y = -2|x - 3| + 3 from the parent function y = |x|.

Back

Reflected over the x-axis, stretched by 2, right 3, up 3.

Front

What is the vertex of the graph of the equation y = -|x + 6|?

Back

(-6, 0)

Front

What does the inequality 3|2x + 7| + 7 < 4 represent?

Back

no solution

Front

How do you graph the absolute value function y = |x|?

Back

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

Front

What is the effect of a negative sign in front of an absolute value function?

Back

It reflects the graph over the x-axis.

Front

What is the general form of an absolute value equation?

Back

y = a|bx + c| + d, where a, b, c, and d are constants.

Front

How do you solve the inequality |x - 4| < 2?

Back

Split into two inequalities: -2 < x - 4 < 2, which gives 2 < x < 6.

Front

What is the domain of the function y = |x + 1| - 4?

Back

The domain is all real numbers, (-∞, ∞).