Exponentials - Lecture notes 34-48 PDF

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Math Units (MTH) Notes...

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Exponentials, Exponentials are comprised of a base and exponent (index or power). The general form is:A⋅enx+b+cA⋅enx+b+c A and n dilate the function b and c translate the function We refer to e as the base and nx + b collectively as the exponent

Exponential,Graphs, The basic shape of an exponential graph is shown below

Graphing,Exponential,Functions, In general, unless told not to, all graphs must provide the coordinates or equations of any: xintercepts, y-intercepts and asymptotes. All exponential functions are presented in a manner somewhat similar to:y=A⋅enx+b+cy=A⋅enx+b+c 1

Asymptote lies at y = c

2

Substitute x = 0 into the equation and solve for y to find the y-intercept

3

Substitute y = 0 into the equation and solve for y to find the x-intercept (not all exponentials will have one).

4

Connect the dots appropriately. Note that the graph must approach the asymptote at one end

5

Adjust the graph according to the domain, finding the coordinates of the endpoints if required. Label with the equation.

Example05.1:0Sketch0y=2ex+1−10labelling0any0x-intercepts0and0yintercepts0with0their0coordinates0and0asymptotes0with0their0equations.E xample05.1:0Sketch0y=2ex+1−10labelling0any0x-intercepts0and0yintercepts0with0their0coordinates0and0asymptotes0with0their0equations.01. 0Sketch0in0the0asymptoteThe0asymptote0lies0at0y=−101.0Sketch0in0the0asym

ptoteThe0asymptote0lies0at0y=−1

02.0Find0the0yinterceptsx=0y=2e0+1−1y=2e1−1y...