SOLUTION: State the domain and range. Explain how you find these mathematically without the use of a graph. (3) y = 20

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Question 1198107: State the domain and range. Explain how you find these mathematically without the use of a graph.
(3) y = 20 - 2x2

(4) y = 25(-7x-4)64

(5) y = x2 / (x2-16)

(6) Let “M” be the set of motor vehicle owners who are registered in Ohio. Let “R” be the set of all motor vehicle registration numbers. Is the correspondence between M and R a function? Why, or why not?

Answer by math_tutor2020(3817) (Show Source):
You can put this solution on YOUR website!

You need to post one question at a time. I'll do problem 3 to get you started.

The domain is the set of all real numbers because we don't have any restrictions on x. We don't have to worry about things like square roots of negative numbers, or dividing by zero. The domain of any polynomial function is always "set of all real numbers".

The smallest x^2 can get is 0.
The largest -x^2 can get is 0, which also applies to -2x^2. Add on 20 to find that the largest y = 20-2x^2 can get is y = 20.
The range is therefore the set of y values such that (either y = 20 or y < 20).

SOLUTION: State the domain and range. Explain how you find these mathematically without the use of a graph. (3) y = 20 - 2x2 (4) y = 25(-7x-4)64 (5) y