How do you find the domain and range of #f(x)= -x^2#?

Question

Ethan Adkins · Accepted Answer

Determine the set of values that the function can possibly have.

The domain and range are a set of values that a function can have - specifically its #x# and #y# value respectfully. Knowing that the function #f(x)=-x^2#, we know that the function has no limit to its #x# variables. As a result, its domain is #{x inRR}. As for the range, there is a limit. If we graph the function, we would see that function can only be #0# or less. Thus, we get a range of #{f(x) inRR | f(x) < 0}#. Just in case, here is the graphed function: graph{-x^2 [-5, 5, 10, 10]} I hope this is helpful.

Abigail Allen · Answer

undefined To find the domain of $ f(x) = -x^2 $, it includes all real numbers since there are no restrictions on the input $ x $.

For the range, since $ f(x) = -x^2 $ represents a downward-opening parabola, the highest point is at the vertex. Since the coefficient of $ x^2 $ is negative, the maximum value occurs at the vertex. Therefore, the range is all real numbers less than or equal to the value of the vertex, which is $ -\infty $.

Jace Anderson · Answer

undefined The domain of $ f(x) = -x^2 $ is all real numbers ($ \mathbb{R} $) because there are no restrictions on the values that $ x $ can take.

The range of $ f(x) = -x^2 $ is all real numbers less than or equal to 0, denoted as $ \{ y \in \mathbb{R} : y \leq 0 \} $. This is because the function $ -x^2 $ will always yield non-positive values, with the maximum value being 0.