Question

Using the integers -5 to 5, at most one time each, write an expression that will have the greatest absolute value.

Options:
a. 5 - x
b. x^2 - 4
c. |x| - 3
d. 2x - 1

Answer 1

The expression with the greatest absolute value is b) x² - 4.

Step-by-step explanation:

To find the expression with the greatest absolute value using the integers -5 to 5 at most one time each, we would evaluate each expression with each integer. By doing so, we can determine which expression yields the largest value when considering the absolute value. Let's evaluate each option with the integers -5 to 5:

a. 5 - x: The absolute values range from 0 to 10.

b. x² - 4: The absolute values range from 4 to 9.

c. |x| - 3: The absolute values range from 2 to 8.

d. 2x - 1: The absolute values range from 1 to 9.

Based on these evaluations, option b. x² - 4 has the greatest absolute value, ranging from 4 to 9.