Question

f(x) = log2(x – 3) + 1
how do you find the domain and the range?

Answer 1

Do you know the transformations of the log function

Answer 2

log2(x)?

Answer 3

the domain is (3,infinity)
When you have just have \[\log_{2} \]
your domain is
(0, infinity)

Answer 4

when you do

you shift the graph to the right 3 units

Answer 5

log2(x-3) i mean

Answer 6

+1 you move up

Answer 7

is there any way of knowing without having to see or make a graph?

Answer 8

Do want an algebraic way?

Answer 9

yes please something that does not require me having to make a graph in order to find the answer

Answer 10

i mean, you dont necessarily gave to graph it. just using knowledge of the log function you know the domain can never be negative. You can just apply the transformations and know generally the shape in your head.

Answer 11

domain is all the possible x values
range is all the possible y values

Answer 12

log of a negative number is defined so
log(x-3) <--- you gotta make sure you dont take log of negative number so
x be 3 or more, if its less its a negative number
so domain(or possible values of x) x>=3,

Answer 13

log of a negative number is undefined

Answer 14

now lets see the lowest point of this log must be at the lowest point of the x

Answer 15

oh sry a slight mistake here!

Answer 16

log(0) is undefined too

Answer 17

so x>3

Answer 18

x=3 is not allowed either

Answer 19

log function goes from -inf to inf