QuestionDetermine the range of the function .
Studdy Solution
STEP 1
Assumptions1. The function given is . We are asked to find the range of the function
STEP 2
The range of a function is the set of all possible output values (y-values), which are determined by the function's domain (x-values).
STEP 3
For a linear function like , the range is all real numbers, because a linear function will cover all y-values as x varies over all real numbers.
STEP 4
However, to confirm this, let's analyze the function. The function is a linear function with a negative slope (-4). This means that as x increases, y decreases, and vice versa.
STEP 5
As x approaches positive infinity, the term -4x becomes increasingly negative, making y increasingly negative. Therefore, there is no lower limit to the values of y.
STEP 6
Similarly, as x approaches negative infinity, the term -4x becomes increasingly positive, making y increasingly positive. Therefore, there is no upper limit to the values of y.
STEP 7
Since there are no upper or lower limits to the values of y, we can conclude that the range of the function is all real numbers.
The range of the function is all real numbers.
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