h(x) = - 3x2 + 2x + 12
answer: all real numbers
How did they get this answer and what does it mean to be all real numbers?

Question

h(x) = - 3x2 + 2x + 12
answer: all real numbers
How did they get this answer and what does it mean to be all real numbers?

solomonzelman · Answer

Do you mean the domain?

bloomlocke367 · Answer

What were they looking for?

helpjebal · Answer

yes it is a lesson on domain of a function

solomonzelman · Answer

The domain is all real numbers, simply speaking, because you can
plug any real number for x into the equation h(x), and get a valid output.

solomonzelman · Answer

Any polynomial, by defnition, will have a domain of "all real numbers".

helpjebal · Answer

so just because it's a polynomial, we know right off the bat that the domain will be "all real numbers" which is 0 and any positive whole number?

solomonzelman · Answer

Think about it logically.

You have whole number powers of x, with some coefficients in front of them,
(+ some number at the end sometimes). No matter what real number you put
in for x, you get a real number back.

there is just simply no reason for the output
to be imaginary if you plug in a real number.

solomonzelman · Answer

You can make an exercise, perhaps....

Make up a polynomial, and plug in some real numbers into the polynomial.
You will always see that your output is going to be a real number.

helpjebal · Answer

thank you! just tried that exercise and it totally worked. Thanks again!

solomonzelman · Answer

You are welcome!