Question

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Answer 1

for these problems think about whether the function is increasing or decreasing as x approaches + infinity or -infinity

let's start with 18

as x approaches + infinity does the function approach + or -infinity?

Answer 2

increases?

Answer 3

actyually

Answer 4

decreases

Answer 5

for the problems you can just observe the highest exponent term

x^3

as x approaches + infinity does x^3 approach + or - infinity?

Answer 6

+

Answer 7

good so the right-end behavior is "f(x) approaches + infinity as x approaches infinity"

how repeat the same process for x approaching - infinity

Answer 8

okay so for #18 it is
-end behavior is "f(x) approaches + infinity as x approaches infinity"

Answer 9

would it be -x then

Answer 10

for 18 you must also consider the left-end behavior

as x approaches -infinity does f(x) approach + or - infinity?

Answer 11

-

Answer 12

good, so the left-end behavior is that f(x) approaches - infinity as x approaches - infinity

Answer 13

for 19 repeat these same two processes, find the end behavior of f(x) as x approaches + infinity and for - infinity

Answer 14

right end is -
left end is +

Answer 15

good, so f(x) approaches - inf when x -> infinity and approaches + infinity when x --> -infinity

Answer 16

that's it