Question

I dont understand why -1 is not in the range of this function??

(x^2-7x+12)/(x-3)

Answer 1

The domain of this function is all real numbers minus the set containing 3 but I am having a brain freeze on why the range is all real numbers minus the set containing -1

Answer 2

what do we get when x = -1?

Answer 3

the range, better yet, what is the value when x = 3?

Answer 4

unless we divide out theat x-3 factor, and then take the limit as x goes to 3?

Answer 5

well when we evleuate at 3 we get zero in the denominator

Answer 6

if we divide out the x-3 factor, then that would be the same as taking the limit as x goes to 3

Answer 7

so, what is the value of the limit? 3-4

Answer 8

is nagtive -1

Answer 9

so, we cant actually "cancel" out like factors in rational expressions, but doing so helps to simplify finding a limit

Answer 10

we can't ever "cancel" out factors anyway, we can simplfy

Answer 11

the domain of the expression does not include 3
the domain of the "simplfied" expression DOES include 3

2 functions are equal if they have the same domain

Answer 12

but yeah, i get what your saying

Answer 13

i just got a brain freeze trying to find out that range, but now i got , thanks

Answer 14

:) good luck

Answer 15

good look to you