How do I graph this f(x) = log 1/4 x.
are you allowed to use calculus?
No
is the function \[f(x) = \log_{\frac{1}{4}}(x)\]
Yes. the (x) is just x
The function log(x) looks like this based on my memory |dw:1345239546908:dw|
well roughly like that
What would the range,domain and general shape be?..
Just come up with some points to sub into x Remember the domain of log(x) is (0,+infinity) 100, 10, 6, 5, 4, 3, 2, 1
you can also think of the graph as a reflection of the graph \(\large y=(\frac{1}{4})^x \) over the line y=x
to type this into your calculator you just put log(100)/log(1/4) = log_(1/4)(100)
What would the range,domain and general shape be?..
the range would be infinity think about it log(x) = y is the same as 10^y = x
notice that y can be any number, whereas x can never be negative
Oh okay, and the domain is all real numbers?
well \[(\frac{1}{4})^y = x\]
can x ever be negative
no
then there is your answer
which is what?
The base of a logarthimic function can never be a negative number?
think about it range is represented by y domain is represented by x
if x can never be negative what does that say about the domain if y can be any value what does that say about the range
the domain is all positive numbers?
yes
but it cannot be zero
but for this equation I would say the domain is all positve numbers and not 0
yes
say x>0
thank you
to plot this by hand, I would change it to \[ (\frac{1}{4})^y= x \] now try numbers for y: y= 1 makes x= 1/4 y= 2 makes x= 1/16 (hmm x is getting closer to 0) plot those points (1/16,2) and (1/4, 1) try making y smaller y=0 , so x= (1/4)^0 = 1 (anything to 0 power is 1) (oh, except 0^0) so (1,0) is a point try y= -1 x= (1/4)^(-1)= 4^1 (flip the fraction)= 4 so (4,-1) try y= -2 x= 4^2= 16 so (16,-2) that is enough to see how it looks
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