Question

What function is graphed below? (graph attached in comments)

f(x) = log (x − 3)
f(x) = log (x + 3)
f(x) = log x + 3
f(x) = log x − 3

Answer 1

Alright @phi is awesome he will help...

Answer 2

okay :)

Answer 3

the key number is what is log(1) ?
if you don't know, what does your calculator say?

Answer 4

logs are confusing (for me, anyway)
but log(1) means what exponent gives us 1?
(we assume base 10)

10 to what power is 1?
the factoid to remember is 10^0 = 1
the power is 0

log(1) means what power gives us 1. and the power is 0
log(1)=0

Answer 5

ah sorry, didn't get a notification that you replied.

Answer 6

assuming you know
log(1)=0
we look for the x value of the graph where it crosses the x-axis (i.e. where y is zero)
what x value is that ?

Answer 7

would it also be 0?

Answer 8

you have to look at the graph. put you finger on the x-axis and move your finger along the x-axis until you reach the curve. then read what x value you are at .
can you do that ?

Answer 9

x=-2

Answer 10

good.

Answer 11

now we have to figure out how to change
log(x) so that it is translated (slid over) from x=1 to x= -2
(because it should be at 0 at x=1, but we see it was moved so that it is at 0 when x=-2)

Answer 12

the "fast way" is to memorize:
to slide a function f(x) to the *left* n steps, write f(x+n)
to slide the function f(x) to the *right* n steps, write f(x-n)

Answer 13

one moment

Answer 14

i figured it out :) thanks!

Answer 15

what did you get ?