Question

Determine whether f(x) approaches negative or positive infinity as x approaches 4 from the left and right.
f(x)= 1/(x-4)^2

Answer 1

\[f(x)=\frac{ 1 }{ x-4^{2} }\]

Answer 2

you know what "x approaches 4 from left" mean?

Answer 3

In the negative direction, correct?

Answer 4

yes,
more precisely, it means

value of x is very very very near to 4 but LESS than 4

like 3.9 or 3.9999999

Answer 5

Okay, and from there I can come to the conclusion that it will be infinitely positive and infinitely negative as x approaches 4 from the left and right?

Answer 6

woah! slow down..

there are 2 cases there

when x approaches 4 from left,

then is x-4 negative or positive??
is (x-4)^2 negative or positive??

based on that you will be able to tell, whether its +infinity or -infinity

Answer 7

similarly, the other case


when x approaches 4 from right,

then is x-4 negative or positive??
is (x-4)^2 negative or positive??

based on that you will be able to tell, whether its +infinity or -infinity

Answer 8

from the right is positive infinity and from the left is negative infinity?

Answer 9

can you first answer these??

is x-4 negative or positive??
is (x-4)^2 negative or positive??

Answer 10

using what values? 3.999?

Answer 11

if you're consider x is approaching from left, then yes

Answer 12

then x-4 would be negative
(x-4)^2 is postive

Answer 13

good!
so for x approaching from left we get positive infinity :)

Answer 14

now take x approaching from right case

Answer 15

then it would be negative infinity

Answer 16

I understand now, sorry for not understanding it until now and thank you for helping me!

Answer 17

welcome ^_^

Answer 18

but actually for right case also, it will be +infinity

Answer 19

because (x-4)^2 will anyways be positive

Answer 20

@Alyssa8

Answer 21

im not that smart lol sorry