SOLUTION: The graph of the basic exponential function (y = bx) has two distinctive characteristics: a) having a y intercept of (0,1), and b) having a horizontal asymptote of y=0.

Question 91830: The graph of the basic exponential function (y = bx) has two distinctive characteristics:

a) having a y intercept of (0,1), and
b) having a horizontal asymptote of y=0.
Since inverse functions have their domains and ranges interchanged, what impact does this have for the graph of y = logb(x
Found 2 solutions by stanbon, Nate:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The graph of the basic exponential function (y = bx) has two distinctive characteristics:

a) having a y intercept of (0,1), and
b) having a horizontal asymptote of y=0.
Since inverse functions have their domains and ranges interchanged, what impact does this have for the graph of y = logb(x)
-------------
y = logb(x) has a vertical asymptote at x=0 and no horizontal asymptote:

==============
Cheers,
Stan H.
Answer by Nate(3500) (Show Source): You can put this solution on YOUR website!
Basic Form: y = a(b^x)
a) having a y intercept of (0,1)
y = a(b^x)
1 = a(b^0)
1 = a(1)
so: y = b^x
b) having a horizontal asymptote of y=0
All exponential equations in the form have a horizontal asymptote as . is defined by any number...
Red Line: b = 2
Green Line: b = 3
Blue Line: b = 4

Since inverse functions have their domains and ranges interchanged, what impact does this have for the graph of y = logb(x).
~ y = b^x ~
Domain: All Reals
Range: y > 0
~ y = logb(x) ~
Domain: y > 0
Range: All Reals
Red Line: b = 2
Green Line: b = 3
Blue Line: b = 4

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