What are the Questions/Outcomes?

1. You will be able to shift, and reflect graphs, and to compress and stretch graphs horizontally and vertically.

2. You will be able to calculate an average rate of change of a function and to interpret its meaning.

3. You will be able to identify one-to-one functions and find and graph their inverses.

4. Do you know the shapes of the graphs of all the parent functions. Be able to recognize when a sufficient portion of the graph is sketched in order to indicate the graph shape.

5. Can you solve any equation containing radicals.

6. Can recognize extraneous solutions?

7. Solve application problems that involve radical equations as part of the solution.

8. Graph a radical function using a table of values.

9. Identify how multiplication can change the graph of a radical function.

10. Identify how addition and subtraction can change the graph of a radical function.

11. Match a radical function to the graph that it represents.

12. Do you understand the difference between a radical and a radicand?

13. Can you rewrite a radical expression by using a rational exponent?

13. How is the power function related to a radical function?

14. How do you identify the restrictions on the domain of a power function that represents a real-word situation?

15. What does the numerator of a rational exponent indicate?

16. How can you rewrite a radical expression as an exponential expression and vice versa?

17. Use a graphing calculator to check your work!

Topic Video Notes

• Simplifying Radical Expressions Without Fractions

• Simplifying Radical Expressions With Fractions

• Simplify Square Roots - Perfect Roots

• Simplify Perfect Nth Roots - Radicals

• Simplify Square Roots - Not Perfect Roots

• Simplify a Radical Expression containing Square Roots in the Numerator and Denominator

• Simplify Radicals with the Same Radicand and Different Indexes

• Simplify a Radical Containing a Fraction - Perfect Root

• Containing Variables

• Simplifying Perfect Nth Roots Containing Variables

• Simplify Radicals Containing Variables With Large Exponents - Not Perfect Roots

• Simplify Radicals with Negative Radicands and Odd Indexes

• Simplify Radicals with Variables - Not Perfect Roots

Multiplying and Dividing Radical Expressions

• Multiplying Radicals Containing Variables

• Multiplying Binomials with Radicals

• Multiplying Conjugates of Radical Expressions

• Review of Multiplying Radicals

• Multiply Square Roots

• Multiply Radicals

• Multiply Radicals

• Multiply Radicals with Variables

• Radicals Raised to Powers

• Distribution with Square Roots

• Multiply Binomials with Square Roots

• Square Binomials With Square Roots

• Rationalize the Denominator of a Radical Expression

• Rationalize the Denominator of a Radical Expression

Rational Exponents

• Write a Radical in Rational Exponent Form

• Simplify Expressions with Rational Exponents

• Simplify an Expression with Rational Exponents and Write in Radical Form

• Simplify an Expression with Negative Rational Exponents and Write in Radical Form

• Multiply and Divide Radicals with Different Indexes Using Rational Exponents - Same Radicand

• Multiply Radicals with Different Indexes Using Rational Exponents - Different Radicand

• Evaluate an Expression with Rational Exponents Using Radicals

• Simplify an Expression with Rational Exponents and Write in Radical Form

• Simplify an Expression with Negative Rational Exponents and Write in Radical Form

Inverse Relations and Functions

• Find an Inverse Function From a Table

• Function and Inverse Function Values Using a Table

• Function and Inverse Function Values Using a Graph

• Restrict the Domain to Make a Function 1 to 1, Then Find the Inverse

• Find Inverse Function Values Without Finding the Inverse Function

• Function and Inverse Function Values

• Find the Inverse of a Square Root Function with Domain and Range

• Find the Inverse of a Rational Function

• Find the Inverse of a Rational Function and an Inverse Function Value

• Determine If Two Functions Are Inverses

• Determine If Two Functions Are Inverses

• Find the Inverse of a Function

• Find the Inverse of a Function

Solving Square Root and other Radical Equations

• Solve a Basic Radical Equation - Square Roots

• Solve Radical Equations - Square Roots

• Solve Radical Equations - Square Roots

• Solve Radical Equations - Square Roots

• Solve Radical Equations - Two Square Roots

• Solve Radical Equations - Two Square Roots

• Solve Radical Equations - Two Square Roots

Graphing Square Root Functions

• Domain and Range of Square Root Functions

• Domain and Range of Radical Functions

• Domain of a Square Root Function with a Quadratic Radicand

• Reflections of the Square Root Function

• Horizontal and Vertical Shifts of the Square Root Function

• Horizontal and Vertical Stretches and Compressions of the Square Root Function

• Match the Graph of a Horizontal and Vertical Shifted Graph to the Function