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# Exponential and Logarithmic Functions

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

by

Tweet## Suzanne Meche

on 14 March 2013#### 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)

Full transcriptPatrick 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)