These are the answers to the various tutorials in Exponential Functions.
Interactive Tutorial Using Java Applet (1)
2  f(x) increases.
3  f(x) increases.
4  f(x) decreases.
5  f(x) decreases.
Interactive Tutorial Using Java Applet (4)
 When a is greater than 1 and increases, the graph is expanded vertically. When a is smaller than 1 and decreases, the graph is shrunk vertcally. When a becomes negative there is also a reflection on the x axis.
 When b is greater than 1 and increases, the graph is shrunk horizontally. When b is smaller than 1 and decreases, the graph is expanded horizontally. When b becomes negative, there is reflection on the y axis.
 When c is positive and increases, the graph is shifted to the left. When c is negative and decreases, the graph is shifted to the right.
 When d is positive and is increased, the graph is shifted up. When d is negative and decreased the graph is shifted down.

The y intercept is given by (0 , f(0)).
f(0) = a*B ^{(b(0+c))} + d
= a*B ^{(b*c)} + d
The parameters that affects the y intercept are: B, a, b, c and d.
Yes, the graph will always have a y intercept.

To find the x intercept, we need to solve f(x) = 0.
a*B ^{(b(x+c))} + d = 0
The above equation can be written
B ^{(b(x+c))} =  d/a
The above equation has solutions only when d/a is positive. Solve the above for x.
b(x+c) = log_{B} (d / a)
x = log_{B} (d / a) / b  c
The parameters that affect the x intercept when it exists are: B, a, b,c and d.
No, the graph will have an x intercept only when d / a is positive .
