find the domain and range in interval notation
f(x)= 3x^5+sqrt7x^3-9x+13

Question

find the domain and range in interval notation
f(x)= 3x^5+sqrt7x^3-9x+13

debbieg · Answer

is it:
$\large f(x)= 3x^5+\sqrt{7x^3}-9x+13$

or:
$\large f(x)= 3x^5+\sqrt{7}x^3-9x+13$
??

anonymous · Answer

bottom

debbieg · Answer

OK, that's easier then. :) Since this is a polynomial, so it well-defined for all real numbers x. That is, there isn't any real number that you can't "plug in" for x. So that should tell you the domain.

debbieg · Answer

with the range, a polynomial with ALWAYS go to either +infinity or -infinity for LARGE values of x.  So if it goes to +infinity on "one end" of the x axis, and -infinity on the other, then you can be sure that the range is all real numbers. (Do you see why?)

The tricky part would be, if you have a polynomial that goes to +infinity at BOTH ends (like, say, $\large y=x^2$  or $\large y=x^6$, or to -infinity at both ends (like, say, $\large y=-x^2$). Then you have to worry about the range having a "maximum" or a "minimum" somewhere, so it ISNT all real numbers.

Now, can you look at this polynomial, and tell what it's doing at the "ends" of the x-axis? E.g., what happens for x's that are very large (as x goes to infinity), or x's that are very small (as x goes to negative infinity)?