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QuestionFind the domain and range of the function f(x)=−43f(x)=-43. Options: A) Domain: {−43}\{-43\}, Range: all reals B) Domain: all reals, Range: {−43}\{-43\} C) Domain: [−43,∞)[-43,\infty), Range: all reals D) Domain: all reals, Range: [−43,∞)[-43,\infty).

Studdy Solution

STEP 1

Assumptions1. The function given is f(x)=−43f(x)=-43 . We need to find the domain and range of this function

STEP 2

First, let's understand what the domain and range of a function are.The domain of a function is the set of all possible input values (often the "x" variable), which produce a valid output from a particular function.
The range of a function is the set of all possible output values (usually the "y" or the value of the function), which come out from the function.

STEP 3

Now, let's analyze the function f(x)=−43f(x)=-43.This is a constant function, meaning that for any value of xx, the output will always be −43-43.

STEP 4

Since the output does not depend on the input, we can say that the domain of the function is all real numbers. This is because we can put any real number into the function and it will still give a valid output.
Domain=All real numbersDomain = \text{All real numbers}

STEP 5

As we mentioned before, no matter what value of xx we input into the function, the output will always be −43-43. Therefore, the range of the function is simply {−43}\{-43\}.
Range={−43}Range = \{-43\}The correct answer is4x B Domain All real numbers, Range {−43}\{-43\}.

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