# Sections 1.4 & 1.5

**Sections 1.4 & 1.5 Inverse Functions, Exponential and logarithmic Functions**

Text for Section 1.4 Inverse Functions

Text for Section 1.5 Exponential and logarithmic Functions

**Learning Outcomes**

- Determine the conditions for when a function has an inverse.
- Use the horizontal line test to recognize when a function is one-to-one.
- Find the inverse of a given function.
- Draw the graph of an inverse function.
- Evaluate inverse trigonometric functions.

- Identify the form of an exponential function.
- Explain the difference between the graphs of xb and bx.
- Recognize the significance of the number e.
- Identify the form of a logarithmic function.
- Explain the relationship between exponential and logarithmic functions.
- Describe how to calculate a logarithm to a different base.
- Identify the hyperbolic functions, their graphs, and basic identities.

Videos

- Inverse Functions
- Determine if a Relation Given as a Table is a One-to-One Function
- Ex 1: Determine if the Graph of a Relation is a One-to-One Function
- Ex: Find an Inverse Function From a Table
- Ex: Find the Inverse of a Square Root Function with Domain and Range
- Ex: Find the Inverse of a Rational Function

- Exponential Function Application (y=ab^x) - Population Growth of India
- Exponential Function Application (y=ab^x) - Population Decline of Chicago
- Exponential Function Application (y=ae^(kt)) - Bacteria Growth
- Compounded Interest
- Graphing Exponential Functions
- Introduction to Logarithms
- Evaluate Natural Logarithms on the Calculator
- Properties of Logarithms
- Graph an Exponential Function and Logarithmic Function
- Solving Exponential Equations Using Logarithms
- Find the Domain of Logarithmic Functions

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