Question

Consider the function h(x) = 3x^3-7x^2+6x-8
What type of function is this? I think it's a polynomial for sure.. um.. could it be exponential, radical, rational, linear?

Answer 1

This is a cubic polynomial function.

Answer 2

Polynomial, cubic, Rational

Answer 3

what makes it rational?

Answer 4

domain and range both all real right?

Answer 5

p(x) = 3x^3-7x^2+6x-8
q(x) = 1
A rational function is p(x)/q(x)

Answer 6

pk that makes as much sense as your name does.

Answer 7

It's polynomial.
For the exponential it means that the exponent is variable

like this:

\[4^{2x}\]

Answer 8

:D thanks Raheen!

Answer 9

But what makes it rational?

Answer 10

Any function h(x) in the form \[h(x)=\frac{f(x)}{g(x)}\] is a rational function where f(x) and g(x) are polynomial functions.


In your case, if f(x)=3x^3-7x^2+6x-8 and g(x)=1, then \[h(x)=\frac{f(x)}{g(x)}=\frac{3x^3-7x^2+6x-8}{1}=3x^3-7x^2+6x-8\], so it's technically a rational function.

Answer 11

but then any quadratic could be rational as well..?

Answer 12

Technically, yes, any quadratic is rational. I would stick to my first answer in saying that it's a cubic polynomial function since that's the most accurate description.

Answer 13

is it also a quadratic?

Answer 14

No, quadratic functions are of degree 2 (ie max exponent is 2), but the max exponent here is 3.

Answer 15

I see. :)