Chapter 14 Discovery 1 Graphs of OnetoOne Functions

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

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

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.

Effect of the Base a on an Exponential Graph Chapter 14 Discovery 3 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

Effect of the Base a on an Exponential Graph Chapter 14 Discovery 3 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 1 a - 1 c, a > 1. The function is increasing/decreasing. The larger the value of a, the steeper/shallower the graph. 8. In exercises 1 d -1 f, 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

Properties of Logarithms Chapter 14 Discovery 4 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 = a 2, the base squared. The logarithms are ____. 9. In exercise 4, x = -1. The logarithms are ____. 10. In exercise 5, x = 0. The logarithms are ____.

Product, Quotient, and Power Rules of Logarithms Chapter 14 Discovery 5 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

Product, Quotient, and Power Rules of Logarithms Chapter 14 Discovery 5 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

Properties of Exponential and Logarithms Equations Chapter 14 Discovery 6 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 e 2 = e 2 is ____. Write a rule for determining a true equation using exponentials. 2. a. If 2 = 2 is true, then log 52 = log 52 is ____. b. If 2 = 2 is true, then log 122 = log 122 is ____. c. If 2 = 2 is true, then ln 2 = ln 2 is ____. Write a rule for determining a true equation using logarithms.