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Exponential functions

Exponential functions. A function in which x is in the power is called an exponential function. Exponent is another name for power. The general form is: y = b ( a x ) where a and b are constants and a is positive. The graph of an exponential function is called an exponential curve.

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Exponential functions

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  1. Exponential functions A function in which x is in the power is called an exponential function. Exponent is another name for power. The general form is: y = b(ax) where a and b are constants and a is positive. The graph of an exponential function is called an exponential curve. An asymptote is a line that a curve approaches, but never touches.

  2. y = 10x y = 3x y = 2x All curves of the form ax pass through the point (0,1) Example 1 Sketch the following curves y = 2x 1/8 ¼ ½ 1 2 4 8 y = 3x 1 3 9 27 0·11 0·33 0·037 • Also sketched is 10x and 1·4x. • As the value of a gets bigger the curve gets: • steeper to the right of the y-axis and • closer to x-axis to the left of the y-axis. • The x-axis is an asymptote. y = 1·4x

  3. y = 3(2x) Example 2 y = 2x Sketch the following curves y = 0·3(2x) 0·3 0·6 1·2 2·4 0·04 0·08 0·15 y = 3(2x) 3/8 ¾ 1½ 3 6 12 24 • Also sketched is 2x. • As the value of b gets bigger in y = b(ax): • the curve gets steeper • The curve cuts the y-axis at b instead of 1. y = 0·3(2x)

  4. Example 3 Today’s work y =1·2(2x) -0·3 -0·6 -1·2 -2·4 -4·8 As b is negative the curve is upside down As b is 1·2 the curve cuts the y-axis at 1·2 -9·6 -0·15 Exercise 12 D page 371 #6, 9, 10, 11

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