Question

Which function has a range limited to the only negative number?

A. f(x)=x²
B.f(x)=eˣ
C. f(x)=−√x
D. f(x)=ln(x)

Answer 1

Among the given functions, f(x) = -√x has a range limited to only negative numbers because the square root of any positive number is non-negative, and when negated, it becomes negative.

Step-by-step explanation:

The function that has a range limited to only negative numbers among the options provided is f(x) = -√x. Let's analyze each function's range:

• f(x) = x² has a range of [0, ∞) because squaring any real number results in a non-negative number.
• f(x) = eˣ has a range of (0, ∞) because the exponential function yields positive values for all real numbers.
• f(x) = -√x has a range of negative numbers because the square root of x (√x) is always non-negative, and when multiplied by -1, it becomes non-positive (negative or zero). However, the square root of zero is zero, so the range excludes zero and is strictly negative.
• f(x) = ln(x) has a range of (-∞, ∞) because the natural logarithm function can take on any real number as its output.

Therefore, the correct answer is C. f(x) = -√x.