OpenStudy (anonymous):

How do I graph this f(x) = log 1/4 x.

6 years ago
OpenStudy (australopithecus):

are you allowed to use calculus?

6 years ago
OpenStudy (anonymous):

No

6 years ago
OpenStudy (australopithecus):

is the function \[f(x) = \log_{\frac{1}{4}}(x)\]

6 years ago
OpenStudy (anonymous):

Yes. the (x) is just x

6 years ago
OpenStudy (australopithecus):

The function log(x) looks like this based on my memory |dw:1345239546908:dw|

6 years ago
OpenStudy (australopithecus):

well roughly like that

6 years ago
OpenStudy (anonymous):

What would the range,domain and general shape be?..

6 years ago
OpenStudy (australopithecus):

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

6 years ago
OpenStudy (anonymous):

you can also think of the graph as a reflection of the graph \(\large y=(\frac{1}{4})^x \) over the line y=x

6 years ago
OpenStudy (australopithecus):

to type this into your calculator you just put log(100)/log(1/4) = log_(1/4)(100)

6 years ago
OpenStudy (anonymous):

What would the range,domain and general shape be?..

6 years ago
OpenStudy (australopithecus):

the range would be infinity think about it log(x) = y is the same as 10^y = x

6 years ago
OpenStudy (australopithecus):

notice that y can be any number, whereas x can never be negative

6 years ago
OpenStudy (anonymous):

Oh okay, and the domain is all real numbers?

6 years ago
OpenStudy (australopithecus):

well \[(\frac{1}{4})^y = x\]

6 years ago
OpenStudy (australopithecus):

can x ever be negative

6 years ago
OpenStudy (anonymous):

no

6 years ago
OpenStudy (australopithecus):

then there is your answer

6 years ago
OpenStudy (anonymous):

which is what?

6 years ago
OpenStudy (anonymous):

The base of a logarthimic function can never be a negative number?

6 years ago
OpenStudy (australopithecus):

think about it range is represented by y domain is represented by x

6 years ago
OpenStudy (australopithecus):

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

6 years ago
OpenStudy (anonymous):

the domain is all positive numbers?

6 years ago
OpenStudy (australopithecus):

yes

6 years ago
OpenStudy (australopithecus):

but it cannot be zero

6 years ago
OpenStudy (anonymous):

but for this equation I would say the domain is all positve numbers and not 0

6 years ago
OpenStudy (australopithecus):

yes

6 years ago
OpenStudy (phi):

say x>0

6 years ago
OpenStudy (anonymous):

thank you

6 years ago
OpenStudy (phi):

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

6 years ago