Graphs of One-to-One Functions

1. Chapter 14 Discovery 1 Graphs of One-to-One Functions In the following graphs of one-to-one functions, draw a horizontal line through more than one point on the graph if possible. 1. 2. Write a rule for determining a one-to-one function from a graph of a function by drawing a horizontal line through points on the graph. 1 of 2

2. Chapter 14 Discovery 1 Graphs of One-on-One Functions Check your rule on the following graph of a function, which is not one-to-one: 3. 2 of 2

3. Chapter 14 Discovery 2 Equivalent Exponential Functions 1. Graph each exponential function on a decimal window. 2. Match the graphs of the functions. Write a rule for determining equivalent functions.

4. Chapter 14 Discovery 3 Effect of the Base a on an Exponential Graph 1. Sketch the graphs of the given exponential functions of the form f(x) = ax, where a > 0, on the same coordinate plane. Use the decimal window. 1 of 2

5. Chapter 14 Discovery 3 Effect of the Base a on an Exponential Graph Use your graphs to complete the following exercises: 2. Determine the domain of each function. 3. Determine the range for each function. 4. Are all the functions one-to-one? 5. Determine the y-intercept of each function. 6. Determine the x-intercept of each function. Choose the correct answer: 7. In exercises 1a - 1c, a > 1. The function is increasing/decreasing. The larger the value of a, the steeper/shallower the graph. 8. In exercises 1d -1f, 0 < a < 1. The function is increasing/decreasing. The smaller the value of a (as a approaches 0), the steeper/shallower the graph. 2 of 2

6. Chapter 14 Discovery 4 Properties of Logarithms Determine the following logarithms in the form logax: 6. In exercise 1, x = 1. The logarithms are ____. 7. In exercise 2, x = a, the base. The logarithms are ____. 8. In exercise 3, x = a2, the base squared. The logarithms are ____. 9. In exercise 4, x = -1. The logarithms are ____. 10. In exercise 5, x = 0. The logarithms are ____.

7. Chapter 14 Discovery 5 Product, Quotient, and Power Rules of Logarithms Approximate each expression, and compare the results obtained in the left column with the corresponding results in the right column. 1. Product rule 2. Quotient rule 1 of 2

8. Chapter 14 Discovery 5 Product, Quotient, and Power Rules of Logarithms Approximate each expression, and compare the results obtained in the left column with the corresponding results in the right column. 3. Power rule Write the following rules of logarithms: 4. Product Rule: 5. Quotient Rule: 6. Power Rule: 2 of 2

9. Chapter 14 Discovery 6 Properties of Exponential and Logarithms Equations Complete the following statements with “true” or “false”: 1. a. If 2 = 2 is true, the 52 = 52 is ____. b. If 2 = 2 is true, then 122 = 122 is ____. c. If 2 = 2 is true, then e2 = e2is ____. Write a rule for determining a true equation using exponentials. 2. a. If 2 = 2 is true, then log52 = log52 is ____. b. If 2 = 2 is true, then log122 = log122 is ____. c. If 2 = 2 is true, then ln 2 = ln 2 is ____. Write a rule for determining a true equation using logarithms.