Question

Describe the end behavior of the function f(x)=7x^4-2x+19 by finding lim f(x) x --> infinity and x--> - infinity

Answer 1

So you need help with function notation? @krlg11

Answer 2

f(x)\[7x ^{4}-2x+19\]

Answer 3

I need help with where to start! I am not even sure how to tackle this!

Answer 4

K I will help u @krlg11

Answer 5

In general, if the degree of the polynomial function f(x) is odd, then

\[\Large \lim_{x\to\infty} f(x) = \infty\]

and

\[\Large \lim_{x\to -\infty} f(x) = -\infty\]

Answer 6

and

if the degree of f(x) is even (f(x) is some polynomial), then

\[\Large \lim_{x\to\infty} f(x) = \infty\]

and

\[\Large \lim_{x\to -\infty} f(x) = \infty\]

Answer 7

so you first need to identify the degree of \[\Large 7x^{4}-2x+19\]

Answer 8

Do they give u the x or do you have to find the x? @krlg11

Answer 9

The degree is 4, which is quartic @jim_thompson5910

Answer 10

the degree is 4 like Comm.Dan is saying


so the degree is even, which means you use this rule


\[\Large \lim_{x\to\infty} f(x) = \infty\]

and

\[\Large \lim_{x\to -\infty} f(x) = \infty\]

Answer 11

So the degree comes from the first part of the equation?

Answer 12

Yes from the first monomial @krlg11

Answer 13

basically what this means is that as x gets bigger in the positive direction, then y gets bigger as well

also x gets bigger in the negative direction, then y gets bigger as well


no matter what, y will always get bigger and head off to infinity

Answer 14

Hmm, okay and knowing that it will equal -infty is just something you have to know?

Answer 15

well you can use a graph to help out

here is some generic odd degree polynomial