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 parent function of absolute value?

Back

The parent function of absolute value is y = |x|.

Front

How does the graph of y = |x| transform to y = |x - 4|?

Back

The graph of y = |x| shifts to the right by 4 units.

Front

What is the first step to solve the equation |x| = 5?

Back

Split into two equations: x = 5 and x = -5.

Front

What does the equation y = -|x| + 1 represent?

Back

It represents a downward-opening V-shaped graph that is shifted up by 1 unit.

Front

How do you solve the inequality |x| < 3?

Back

Split into two inequalities: -3 < x < 3.

Front

What is the effect of multiplying the absolute value function by a negative number?

Back

It reflects the graph across the x-axis.

Front

What is the equation of the graph that opens upwards and is shifted up by 1 unit?

Back

f(x) = |x| + 1.

Front

How do you isolate the absolute value in the equation |x| + 5 = 10?

Back

Subtract 5 from both sides to get |x| = 5.

Front

What is the solution set for the inequality |x - 2| > 3?

Back

x < -1 or x > 5.