Question 91830
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 {{{y = a(b^x)}}} have a horizontal asymptote as {{{y = 0}}}. {{{b}}} is defined by any number...
Red Line: b = 2
Green Line: b = 3
Blue Line: b = 4
{{{graph(300,200,-6,6,-1,6,2^x,3^x,4^x)}}}
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
{{{graph(300,200,-1,6,-6,6,log(2,x),log(3,x),log(4,x))}}}