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Sketching exponential functions summary

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Mathematics Teaching for Learning
Engineering Maths B, Exponents
September 20th, 2008 by Craig Rose
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Engineering Maths B, Exponents
September 20th, 2008 by Craig Rose
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As discussed in graphs of exponential functions the most informative approach is to view the general form

$y=ae^{b\left(x-c\right)}+d$

as a set of transformations.

These transformations are summarised here in tabular form.

$y=ae^{b\left(x-c\right)}+d$
Term	Transformation	Features
$a$	Dilation in Y-direction	If $c=0$ and $d=0$ (ie no Translation) the y-intercept is $\left(0,a\right)$
$a<0$	Reflection in X-axis
$b$	Dilation in X-direction	If $c=0$ and $d=0$ (ie no Translation) the y-intercept is $\left(0,1\right)$
$b<0$	Reflection in Y-axis
$c$	Translation in X-direction	If $a=1$ , $b=1$ and $d=0$ (ie no other transformastions) the y-intercept is $\left(0,e^{-c}\right)$
$d$	Translation in Y-direction	Asymptote at $y=d$