1. Restricted Values 1. Complete the following tables of values for the given radical functions: x -3 -2 0 1 -3 -2 0 1 -3 -2 0 1 -3 -2 0 1 1 of 2 Chapter 13 Discovery 1 f(x) x x x j(x) g(x) h(x)

2. 2 of 2 Restricted Values 2. Determine the restricted values of each function if possible. 3. The functions in exercise 1a and 1b are defined by even roots. The functions in exercises 1c and 1d are defined by odd roots. Which functions have restricted values? 4. Graph the given radical functions with restricted values on a decimal calculator screen. Trace each function’s graph. What happens when you reach the restricted x-values you found in exercise 2. 5. Write a rule for determining the restricted values of a radical function by viewing its table of values. 6. Write a rule for determining the restricted values of a radical function by viewing its graph. 7. Write a rule for determining the restricted values of a radical function algebraically. Chapter 13 Discovery 1

3. Radical and Rational Exponents Evaluate each expression, and compare the results obtained in the left column with the corresponding results in the right column. Write a rule for writing a radical expression as an exponential expression. Chapter 13 Discovery 2

4. More Radical and Rational Exponents Evaluate each expression, compare the results obtained in each row. Write a rule for converting an expression with a rational exponent to a radical expression. Chapter 13 Discovery 3

5. Conjugates Multiply and simplify. What did you notice about the products? Chapter 13 Discovery 4

6. Powers of i 1. Evaluate the following expressions: i 1 = i 2 = a. i 3 = ___ b. i 4 = ___ c. i 5 = ___ d. i 6 = ___ 2. Look for a pattern and predict the following: i 7 = ___ Check your prediction on your calculator. Were you correct? The calculator value is written in scientific notation. If you evaluate the calculator value, it should be approximately -i. 3. Predict a value for i 8 and check your value again. i 8 = ___ Look for a pattern and then write a rule for evaluating i to any power. Chapter 13 Discovery 5 i