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

1 Answer
Oct 29, 2016

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]}