Question

How do you sketch the graph of `y=log_(1/2)x` and `y=(1/2)^x`?

Answer 1

See the explanation and the Socratic graphs.

Explanation:

The inverse of the second is `x=log_(1/2)y` and the graphs of these

two are one and the same...

But the first is got from the second by the swapping

`(x, y) to (y, x)`..

Conventionally ( traditionally ), many call each of the given relations

as the inverse relation for the other.

Separately, each graph can be obtained from the other by rotation

through `-or+90^o`, about the origin.

Graph of `y = log_(1/2)x`:

x = 0 ( y-axis) is asymptotic and `x>0`...
graph{y+1.44 ln (x)=0[0 20 -5 10]}

A short Table for the second `y=(1/2)^x` is

`(x, y):`

`(-oo, oo)...(.-5, 32) (-4, 16) (-8, 3) (-4, 2), (-1, 2) (0, 1)`

`(1, 1/2) (2, 1/4) (3, 1/8) (4, 1/16) (5, 1/32) ...(oo, 0)`

Graph of `y = (1/2)^x`:

y = 0 ( x-axis ) is asymptotic and `x>0`..
graph{ y-(0.5)^x=0[-5 25 -10 10]}