Question

What is the range of the absolute value function below?

f(x) > -4
f(x) = -1
f(x) < 1
f(x) < 4

A) f(x) > -4
B) f(x) = -1
C) f(x) < 1
D) f(x) < 4

Answer 1

The range of the absolute value function includes only non-negative values, hence option A) f(x) > -4 is the correct answer as it implies that the value of the function is above -4 and can include zero and all positive values.

Step-by-step explanation:

The question asks for the range of the absolute value function. By definition, absolute value functions always yield non-negative results because they measure the distance a number is from zero on the number line, regardless of direction. Therefore, the output of an absolute value function cannot be negative. So, when presented with the options given, the correct answer for the range of the absolute value function is f(x) > -4.

Considering that the absolute value of any real number is always greater than or equal to zero, the range of the absolute value function can only include values that are zero or greater. Hence, the answer A) f(x) > -4 is the only choice that is always correct for the range of the absolute value function, since all real values of f(x) will be greater than -4.