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By Marcel B. Finan

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Reflections about the y-axis: For a given function f (x), the graph of f (−x) is a reflection of the graph of f (x) about the y-axis. Vertical Stretches and Compressions: If a function f (x) is given, then the graph of kf (x) is a vertical stretch of the graph of f (x) by a factor of k for k > 1, and a vertical compression for 0 < k < 1. What about k < 0? If |k| > 1 then the graph of kf (x) is a vertical stretch of the graph of f (x) followed by a reflection about the x-axis. If 0 < |k| < 1 then the graph of kf (x) is a vertical compression of the graph of f (x) by a factor of k followed by a reflection about the x-axis.

After n periods, is B =P 1+ r n n . If the investment extends to another year than the balance would be given by r 2n P 1+ . n For an investment of t years then balance is given by B =P 1+ Since 1 + r n nt = 1+ r n n t r n nt . then the function B can be written in the form B(t) = P at where a = 1 + r n n . That is, B is an exponential function. g. ”in name only”). When interest is compounded more frequently than once a year, the account effectively earns more than the nominal rate. Thus, we distinguish between nominal rate and effective rate.

N For an investment of t years then balance is given by B =P 1+ Since 1 + r n nt = 1+ r n n t r n nt . then the function B can be written in the form B(t) = P at where a = 1 + r n n . That is, B is an exponential function. g. ”in name only”). When interest is compounded more frequently than once a year, the account effectively earns more than the nominal rate. Thus, we distinguish between nominal rate and effective rate. The effective annual rate tells how much interest the investment actually earns.

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