Determine both the domain and the range of the function. $y = f ( x ) = - 5 | x |$
A)Domain: the set of real numbers greater than or equal to 0. Range: the set of real numbers.
B)Domain: the set of real numbers. Range: the set of real numbers less than or equal to 0.
C)Domain: the set of real numbers less than or equal to 0. Range: the set of real numbers.
D)Domain: the set of real numbers. Range: the set of real numbers greater than or equal to 0.
E)Domain: the set of real numbers greater than or equal to 0. Range: the set of real numbers less than or equal to 0.

Question

Quizplus · Accepted Answer

The absolute value function $|x|$ can take any real number as input, making the domain all real numbers. The output is always non-negative, but the multiplication by -5 flips the sign, making all outputs non-positive. Hence, the range is all real numbers less than or equal to 0.

Determine Both the Domain and the Range of the Function y=f(x)=−5∣x∣y = f ( x ) = - 5 | x |y=f(x)=−5∣x∣

Determine Both the Domain and the Range of the Function $y = f ( x ) = - 5 | x |$