Question

how do you determine the range of a function?

ex.
a. f(x)=12x+3
b. g(x)=1/x^2
c. h(x)=square root of(5x-7) +4

Answer 1

\[c. h(x)= \sqrt{5x-7}+4\]

Answer 2

most of the time you can find the inverse of the function and look at its domain.
y = 12x+3
(y-3)/12 = x domain is all R so range of 12x+3 is all real

Answer 3

what do you mean by "domain is all R so range of 12x+3 is all real"? how did you get that

Answer 4

the domain of (y-3)/12 is what?

Answer 5

x?

Answer 6

domain is numbers not variables. wht numbers can y be?

Answer 7

well it can be a variable but dont think about that right now

Answer 8

but as a number it can be anything

Answer 9

yes, so we found the inverse function and its domain to be R so the originals functions range is all R

Answer 10

I should say relation and not function

Answer 11

so the range to any function with no fraction and no square root is all real numbers?

Answer 12

no it could have a log
most of the time the problem comes from 1/x sqrt(x) and ln(x) ... most of the time.

Answer 13

ok anyway what about B how do you get the range when there's a fraction?

Answer 14

I did that one, read up ^.

Answer 15

y = 1/x^2
x^2 = 1/y
x = +-sqrt (1/y) so 1/y must be >0 so y is all posotive numbers thus the range of 1/x^2 is all positive numbers