# Answers to Tutorials in Exponential Functions

These are the answers to the various tutorials in Exponential Functions.

### Interactive Tutorial - Part 1

2 - f(x) increases.
3 - f(x) increases.
4 - f(x) decreases.
5 - f(x) decreases.

### Interactive Tutorial - Part 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 increases, 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. When 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) = logB (-d / a)

x = logB (-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 .