Question

Use complete sentences to analyze the graph of the function f(x) = log 1/4 x.

Part 1 : Describe the domain, range, and general shape of this graph.

Part 2 : Using complete sentences, explain how plotting specific points helps graph the function and note any critical points such as its intercepts

Answer 1

The relation is like this: \(\normalsize\color{blue}{ \log_{\large A}B=C~~~~~⇒~~~~~A^{\large C}=B }\)

Answer 2

1/4 is the base right ?

Answer 3

yes

Answer 4

So, then \(\normalsize\color{blue}{ y=\log_{\Large \frac{1}{4}}x~~~~~⇒~~~~~\Large{(}\Large \frac{1}{4})^{\large y}=x }\)

Answer 5

oh ok

Answer 6

you can see that as
x→∞, y→ 0 and when x→ -∞ y→ ∞

Answer 7

We learned the domains and ranges like for example: y<1.

Answer 8

wait, but I still not understanding part 2.

Answer 9

@SolomonZelman can you continue?

Answer 10

@paki @mathstudent55

Answer 11

@SolomonZelman please have a look here...

Answer 12

will just say that for example,

(1/4) ^ y = x
(1/4) ^ (1) = 1/4
and (1/4) ^ (2) = 1/16
and (1/4) ^ (3) = 1/64

This is what I was talking about when I said `y→∞, x→0`.

The other way,
(1/4) ^ (-1) = (4/1) ^ 1 = 4
(1/4) ^ (-2) = (4/1) ^ 2 = 16
(1/4) ^ (-3) = (4/1) ^ 3 = 64 and so on, saying that `y→ -∞, x→0`

Y-intercept
(1/4) ^ (0) = x
x=1

X-intercept
(1/4) ^ (y) = 0
y = no solution, because there is no number N, such that `(not a zero)^ N = zero.`