Solving Absolute Value & Graphs 2025

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?

Back

To solve an equation of the form |A| = B, you set up two separate equations: A = B and A = -B.

Front

What is the graph of an absolute value function?

Back

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

Front

What does the equation |x - 3| = 5 represent?

Back

It represents two equations: x - 3 = 5 and x - 3 = -5, leading to solutions x = 8 and x = -2.

Front

How many solutions does the equation |x + 4| = 0 have?

Back

It has one solution, x = -4, since the absolute value can only equal zero at one point.

Front

What is the effect of adding a constant outside the absolute value?

Back

Adding a constant outside the absolute value shifts the graph vertically. For example, |x| + 2 shifts the graph of |x| up by 2 units.

Front

What is the solution set for |2x + 3| = 7?

Back

The solution set is x = 2 and x = -5.

Front

What does the equation |c - 7| = 2 imply about c?

Back

It implies that c can be either 9 or 5, since c - 7 = 2 or c - 7 = -2.

Front

How do you determine the number of solutions for |x - 1| = k where k > 0?

Back

There are always two solutions for k > 0: x - 1 = k and x - 1 = -k.

Front

What is the solution to the equation |-3x + 6| = 12?

Back

The solutions are x = -2 and x = 6.