Sketch the graph of polynomial functions with the following characteristics.

Question

An odd function with zeros at -1,2 and 5 and a negitive leading coefficient.

Answer 1

The "zeros" are just your x-intercepts, so plot those points first. If the function is odd, that means f(-x)=f(x); in other words, it's symmetric about the origin (which just means when you flip your paper upside down, the graph looks the same). Given the zeros, it technically can't be odd, so maybe the question meant to say that the degree is odd? Assuming that's the case, an odd degree (highest exponent on a variable in the function) tells you about the end behavior. If the degree of the polynomial is odd, one end of the graph will go down and the other will go up; if the degree of the polynomial is even, both ends of the graph will go up or both will go down. The sign of the leading coefficient (number in front of the degree variable, which isn't necessarily first) tells you which way the ends go. For a polynomial with an odd degree and a positive leading coefficient, the ends of the graph would fall on the left and rise on the right. And that's flipped if the leading coefficient is negative. They didn't give you any other details so as long as you have the correct zeros and end behavior, you can just make up the rest since it says "sketch." I hope this helps!