How would the domain and range of the function y = one-fourth x minus 6 be determined? Explain.

For a given function f(x), we define the domain as the set of the possible inputs of the function and the range as the set of the outputs of the function.

We will see that both domain and range are the set of all real numbers.

D = (-∞, ∞)

R = (-∞, ∞)

Here we have the function:

The first thing we need to do is find the domain.

We start by assuming that the domain is the set of all real numbers and then we try to find some given values of x that cause some undefined operation, and then we remove these values of x from the domain.

Where this would be something like a zero in the denominator or something like that. We also could have specific restrictions to the domain that are applied in some specific cases (for example if x represents a length we should remove the negative values from the domain).

Here we can see that we do not have any indetermination, thus the domain is the set of all real numbers.

Now to study the range we need to see the general function, we can see that as x tends to negative infinity y will also tend to negative infinity, while when x tends to infinity y will also tend to infinity.

Then the range will also be the set of all real numbers.

If you want to learn more, you can read:

link

Domain (-∞, ∞)

Range (-∞, ∞)

Step-by-step explanation:

y = 1/4x - 6

The domain is all possible values for x.

The range is all possible values for y.

Picture the graph of this function: are there any discontinuities, like asymptotes or holes? If this answer is no (which it is), then the domain and range are unbounded and go from negative infinity to infinity.

10 glasses of juice could be made with 5 carrots, 1,500 orange juice, 2,000 papaya juice.

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