Section 9.1: Evaluating Radical Expressions and Graphing Square Root and Cube Root Functions.

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Presentation transcript:

Section 9.1: Evaluating Radical Expressions and Graphing Square Root and Cube Root Functions

9.1 Lecture Guide: Evaluating Radical Expressions and Graphing Square Root and Cube Root Functions

The natural number n is the index or the order of the radical. Radical Notation denotes the principal nth root of x x is the radicand. is the radical symbol, or the radical. The natural number n is the index or the order of the radical.

Principal Square Root Algebraically Verbally Numerically For any real number : if and denotes the principal square root of x. Graphically by

Principal Cube Root Algebraically Verbally Numerically For any real number x: Graphically if y is a real number and denotes the principal cube root of x. by

Objective: Evaluate radical expressions.

Evaluate each expression. Use a calculator only to check your answer

Evaluate each expression. Use a calculator only to check your answer

Evaluate each expression. Use a calculator only to check your answer

Evaluate each expression. Use a calculator only to check your answer. 7.

Evaluate each expression. Use a calculator only to check your answer. 8.

Evaluate each expression. Use a calculator only to check your answer. 9.

Evaluate each expression. Use a calculator only to check your answer. 10.

Objective: Graph square root and cube root functions.

11. Type: x-intercept: y-intercept: Domain: Range: Table Graph

12. Type: x-intercept: y-intercept: Domain: Range: Table Graph

Objective: Determine the domain of a square root function.

Domain of a Function The domain of a real-valued function set of all real numbers for which is the ____________________ ____________________ under a is also a real number. This means the domain excludes all values that cause division by ____________________ or cause a square root symbol.

13.Determine the domain of using a calculator. Then graph without a window of using by to verify your result.

14.Determine the domain of using a calculator. Then graph without a window of using by to verify your result.

Determine the domain of the following. Use a graphing calculator only as a check on your work. 15.

Determine the domain of the following. Use a graphing calculator only as a check on your work. 16.

Determine the domain of the following. Use a graphing calculator only as a check on your work. 17.

Determine the domain of the following. Use a graphing calculator only as a check on your work. 18.

19.Givenevaluate each expression without a calculator.