Question

Choose the end behavior of the graph of each polynomial function.

Answer 1

image link: https://images.slideplayer.com/27/9162858/slides/slide_2.jpg

Answer 2

this chart will help guide you in finding the end behavior of a function. I will do part a) for you to demonstrate how to use such a chart. then, you can practice b) and c) on your own, and tell me if you get stuck.

a) f(x) = 2x^4 - 6x^3 + 7x + 8

let's look at the term with the highest exponent. 2x^4 has the exponent 4 which makes it the highest out of the whole expression.

the degree (highest exponent) is 4, so it's even.
additionally, the sign of the leading coefficient (2) is positive.

therefore, it falls under the first row on our chart. which means that as x ---> positive infinity, f(x) ---> positive infinity
and as x ----> negative infinity, f(x) ----> positive infinity

so that's the end behavior for part a

repeat this process for functions b and c. however, something to note for function c: you'll have to expand the function first, then perform the analysis.