Absolute Value Test 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| = a when a < 0?

Back

There is no solution because absolute values cannot be negative.

Front

What does the equation |x - 6| = 0 represent?

Back

It represents the point where x is exactly 6, as the absolute value is zero only when the expression inside is zero.

Front

How do you solve the equation |x + 5| = 3?

Back

You set up two equations: x + 5 = 3 and x + 5 = -3, leading to solutions x = -2 and x = -8.

Front

What is the graphical representation of an absolute value function?

Back

An absolute value function creates a V-shaped graph that opens upwards, with the vertex at the point where the expression inside the absolute value equals zero.

Front

What is the solution to the inequality |x| < a when a > 0?

Back

The solution is -a < x < a, meaning x is between -a and a.

Front

What happens to the inequality sign when you multiply or divide by a negative number?

Back

The inequality sign flips direction.

Front

What is the domain of the function f(x) = |x|?

Back

The domain is all real numbers, as you can input any real number into the absolute value function.

Front

What is the range of the function f(x) = |x|?

Back

The range is y ≥ 0, as absolute values cannot be negative.

Front

How do you express the maximum and minimum allowable weights of a chocolate bar that should weigh 6 oz with a variation of 0.02 oz?

Back

The equation is |x - 6| = 0.02, where x represents the weight of the chocolate bar.