Question

find the end behavior
f(x)=(x-3)(1-x)(3x-5)
Lim f(x) lim f(x)
x--> infinity x--> negative infinity

Answer 1

After expanding
\[
f(x)=(1-x) (x-3) (3 x-5)\\
f(x)=-3 x^3+17 x^2-29 x+15\\
\]

Answer 2

A polynomial near Infinity behaves like its term of highest degree, meaning like
\[- 3 x^3
\]
Hence it approaches -Infinity when x approaches Infinity and
it approaches xxx when x approaches -Infinity. Can you find what xxx is?

Answer 3

xxx?

Answer 4

It means find the limit of f(x) when x approaches - Infinity

Answer 5

ok so the answer would be infinity?

Answer 6

Yes when x approaches - Infinty

Answer 7

ok how did you find that?
im really confused

Answer 8

How much is
\[
- 4 x^3
\]
When x =-10, x=-100, x = - 1000?

Answer 9

ok thanks

Answer 10

Did you understand what is going on?