Question

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

Answer 1

are you allowed to use calculus?

Answer 2

No

Answer 3

is the function

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

Answer 4

Yes. the (x) is just x

Answer 5

The function log(x) looks like this based on my memory

Answer 6

well roughly like that

Answer 7

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

Answer 8

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

Answer 9

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

Answer 10

to type this into your calculator you just put

log(100)/log(1/4) = log_(1/4)(100)

Answer 11

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

Answer 12

the range would be infinity

think about it

log(x) = y
is the same as
10^y = x

Answer 13

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

Answer 14

Oh okay, and the domain is all real numbers?

Answer 15

well

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

Answer 16

can x ever be negative

Answer 17

no

Answer 18

then there is your answer

Answer 19

which is what?

Answer 20

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

Answer 21

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

Answer 22

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

Answer 23

the domain is all positive numbers?

Answer 24

yes

Answer 25

but it cannot be zero

Answer 26

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

Answer 27

yes

Answer 28

say x>0

Answer 29

thank you

Answer 30

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