Question

without graphing, describe the end behavior of the graph of the function f(x)=3x^3

Answer 1

the exponent is odd, hence

Answer 2

actually that is not complete
the exponent is odd AND the leading coefficient is positive (it is 3)

Answer 3

my options look like this\[A s x--->\infty, f(x)--->-\infty\]

Answer 4

@satellite73

Answer 5

Well the greatest degree determines the end behaviour, in your case the degree is 3 (cube) since you have \[y=3x^3 \] and your degree is odd, so we look at the ends of the graph (that's why it's called end behaviour). So if we plug infinity/ - infinity in our function, then f(x) will go to positive infinity and negative infinity

Answer 6

That's what it means by x-> infinity, so if you plug in larger numbers in the equation you will get a larger number, in this case f(x) = infinity, and since it's odd, if you plug in x-> - infinity then f(x) = - infinity, hope that makes sense!

Answer 7

So notice odd degrees have two end behaviours