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Answers to Tutorials in Exponential Functions

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)

  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 .

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