Answers to 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)

1. 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.
   
2. 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.
   
3. When c is positive and inceases, the graph is shifted to the left. When c is negative and decreases, the graph is shifted to the right.
   
4. When d is positive and is increased, the graph is shifted up. Whed d is negative and decreased the graph is shifted down.
   
5. 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.
   
6. 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 .