Restricted Values Chapter 13 Discovery 1 1 Complete

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

Restricted Values Chapter 13 Discovery 1 2. Determine the restricted values of each function if possible. 3. The functions in exercise 1 a and 1 b are defined by even roots. The functions in exercises 1 c and 1 d 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. 2 of 2

Radical and Rational Exponents Chapter 13 Discovery 2 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 3 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.

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

Chapter 13 Discovery 5 Powers of i 1. Evaluate the following expressions: i 1 = i i 2 = a. i 3 = ___ c. i 5 = ___ -1 b. i 4 = ___ 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.