Question

What function is graphed below?

Answer 1

Explanation:

This is a concept as opposed to knowing EXACTLY what the equation of the graph is. All we have to be concerned about here is whether it is even or odd, and whether it is positive or negative.

This is not an even function. The first 2 choices aren't what you're looking for. Even functions have tails that both go the same way, either both up or both down. That means that it is an odd function. When an odd function is positive, the left tail goes down and the right tail goes up; when an odd function is negative, the left tail goes up and the right tail goes down. Since our left tail goes down and our right goes up, this is clearly a positive odd function. The last choice is the one you want.

Learn about "end behavior". That's what this is all about. That, and positive and negative functions.

Answer 2

`y=5x^5`

Explanation:

Functions of the form:

`f(x)=cx^n,\hspace{8}c\\eq0,\hspace{8}n\geq1`

There are two cases with these kind of funtions:

First case:

n is even:

If n is even and c>0 the function tends to ∞. On the other hand, if n is even and c<0 the function tends to -∞. The range in every case is:

`n=even,\hspace{6}c>0\\R=[0,\infty)\\\\n=even,\hspace{6}c<0\\R=(-\infty,0]`

Second case:

n is odd:

If n is odd and c>0 the function tends to ∞ for every x>0 and tends to -∞ for every x<0. On the other hand If n is odd and c<0 the function tends to -∞ for every x>0 and tends to ∞ for every x<0. The range in every case is:

`n=odd,\hspace{6}c>0\\R=(-\infty,\infty)\\\\n=odd,\hspace{6}c<0\\R=(-\infty,\infty)`

According to this the first two option doesn't fit with the graph because n=2=even. So it must be the last two options. As you can see the graph tends to ∞ for every x>0 and tends to -∞ for every x<0, hence c>0.

Therefore the answer is:

`y=5x^5`

I attached you the graph in order that you can corroborated the answer.