SOLUTION: What is the domain and range of the function f(x)=-2x-7. And how do you get those answers?

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Question 968878: What is the domain and range of the function f(x)=-2x-7. And how do you get those answers?
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
When finding the domain you ask the question:

Are there any numbers that cannot be substituted for x?

If the answer is "no", then the DOMAIN is %28matrix%281%2C3%2C-infinity%2C%22%2C%22%2Cinfinity%29%29

If the answer is "yes", then exclude any such numbers from the DOMAIN.

When finding the range, replace f(x) by y.  Solve for x.

Ask the question:

Are there any numbers that cannot be substituted for y?

If the answer is "no", then the RANGE is %28matrix%281%2C3%2C-infinity%2C%22%2C%22%2Cinfinity%29%29

If the answer is "yes", then exclude any such numbers from the RANGE.

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In your problem, ask the question:

Are there any numbers that cannot be substituted for x in f(x)=-2x-7?

The answer is "no" because there are no denominators to become 0,
and there are no square roots to have negative numbers under them.

So the domain is %28matrix%281%2C3%2C-infinity%2C%22%2C%22%2Cinfinity%29%29

Replace f(x) by y

y = -2x-7
 Solve for x

2x = -y-7
 x = %28-y-7%29%2F2

Ask the question:

Are there any numbers that cannot be substituted for y?

The answer is "no" because there are no denominators to become 0, since
the only denominator is the constant 2.  There are no square roots to have
negative numbers under them.

So the RANGE is %28matrix%281%2C3%2C-infinity%2C%22%2C%22%2Cinfinity%29%29

Edwin