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# Exponential and Logarithmic Functions

Notes on the inverse relationship, properties, graphing, and transformations.
by

## Suzanne Meche

on 14 March 2013

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#### Transcript of Exponential and Logarithmic Functions

Transformation Demo - very detailed. Note how he uses different letters for the vertical and horizontal translations as well as a dilation factor applied directly to 'x' that is also a horizontal compression. Some basics... Simple and Compound Interest -
Patrick JMT explains all... family: exponential function
parent: f(x)= ab^x
transformation: f'(x)= ab^(x-h) + k Transformations Cool explanation that utilizes the inverse relationship between logs and exponents so you don't have to use the change of base formula Real Life Application a logarithm is the number of times a base is multiplied by itself to obtain a specific number We use functions that fit and best describe the nature of data.
In this case it's the % volume
of hydrocarbons/minute Exponential and Logarithmic Functions
An Inverse Relationship Logarithmic Function Exponential Function exponent - the number of times a base factor is multiplied by itself
base - the factor that is multiplied repeatedly; think of it as the number that holds up the exponent family: logarithmic function
parent: f(x)= alogb x
transformation: f'(x)=alogb(x-h) + k Graphing Exponential Functions
Graphing Logarithmic Functions Graphing the Inverse Functions Real World Applications Another example - The Sichuan Province Earthquake Properties of Logarithmic Functions -
How to +, -, x, / and raise to a power:
From YayMath! Describe Bacterial Growth Common Uses Graphing Activity for Base 10 Exponent and Log:
1) Make an Input/Output Table for f(x)= 10^x
for x = -2, -1, 0, 1, 2
2) Graph the points (you'll have to estimate)
and the asymptote.
3) Make an Input/Output Table for f(x) = log x
for x = -2, -1, 0, 1, 2. What do you notice
about the negative values for x?
What do you notice about the
relationship between the input and output
for the exponential function and the
input and output for the log function?
4) Graph the log function by first sketching the
asymptote and x-intercept. Estimate the curve. Graphing Activity for Base e Exponent and Log:
1) Make an Input/Output Table for f(x)= e^x
for x = -2, -1, 0, 1, 2
2) Graph the points (you'll have to estimate)
and the asymptote.
3) Make an Input/Output Table for f(x) = ln x
for x = -2, -1, 0, 1, 2. What do you notice
about the negative values for x?
What do you notice about the
relationship between the input and output
for the exponential function and the
input and output for the ln function?
4) Graph the ln function by first sketching the
asymptote and x-intercept. Estimate the curve. Oblique Asymptote inverse function - a function that 'undoes' another function; the domain and range of the original function are the range and domain of its inverse function

asymptote (Gr) - not falling together, linear: horizontal (parallel to the x-axis), vertical (parallel to the y-axis), oblique(at an angle to the axes)
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