Absolute Value Functions and Word Problems 2

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 express a tolerance range using absolute value?

Back

A tolerance range can be expressed as |x - c| ≤ t, where c is the target value and t is the tolerance.

Front

What does the inequality |b - 5| ≤ 0.2 represent?

Back

It represents that the value b is within 0.2 units of 5, meaning b can be between 4.8 and 5.2.

Front

What is the solution set for the equation |x - 6| < 4?

Back

The solution set is 2 < x < 10.

Front

What does it mean if an absolute value inequality is an 'and' problem?

Back

It means the solution must satisfy both conditions simultaneously, typically represented as a range.

Front

Write an absolute value equation for having 50 dollars give or take 15.

Back

|x - 50| = 15.

Front

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

Back

The solutions are x = 12 and x = 0.

Front

Can you use the symbols [ or ] with infinity?

Back

No, you cannot use [ or ] with infinity; infinity is always represented with ( or ).

Front

What is the graphical representation of an absolute value function?

Back

An absolute value function graphs as a V-shape, opening upwards.

Front

How do you solve an absolute value equation like |x| = a?

Back

You solve it by setting up two equations: x = a and x = -a.