Sections 1.4 & 1.5

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