1. Quiz 6-4 1. 2. 4. Are the following functions inverses of each other ? (hint: you must use a composition each other ? (hint: you must use a composition to prove it). to prove it). (-2, 5), (5, 6), (-2, 6), (7, 6) What is the inverse relation of: Find the inverse of: y = 0.5x + 2 3.

2. Quiz 6-2 Rationalize the Denominator 1. 3. 2.

3. The Square Roof Function (Input) x(rule) (output) f(x) f(x) 00 1 2 3 4 5 6 7 +y+y+y+y +x+x+x+x 8

4. Section 6-5 Graphing Radical Equations. Your turn: Graph the following on your calculator: 1. What is the domain of the function? 2. What is the range of the function? 3. (don’t delete the first equation): graph the following then select the correct answer from the 3 following choices: select the correct answer from the 3 following choices: a. It is the graph of shifted up 2, and left 3. b. It is the graph of shifted down 3, and right 2. c. It is the graph of shifted down 3, and left 2.

5. Section 6-6 Solve Radical Functions

6. Vocabulary Radical Equation: An equation with a radical symbol in it. symbol in it.

7. Review (Solving single variable equations) 10 = 3x – 2 What does it mean to solve an equation ? “use properties of equality to get the variable on one side of the equal sign variable on one side of the equal sign and every other number on the other side.” and every other number on the other side.” + 2 12 = 3x 12 = 3x ÷ 3 4 = x

8. Solving an Exponential Equation (Review Section 6-2) ÷2÷2 Isolate the base and its exponent. exponent. “undo” squaring (turn the exponent into a ‘1’) into a ‘1’) Even Root !!!  ± result x = 6, 2

9. Your Turn: Solve for ‘x’ 4. 5.

10. Now solve a radical equation. Remove the radical by squaring each side -6 -6 x = 3 Isolate ‘x’ on one side of the equal sign by of the equal sign by subtracting 6 from both sides. subtracting 6 from both sides.

11. Using Exponent Form (may be easier) “undo” square root  square both sides Solve for ‘x’ x = 3

12. Your Turn: 6. 7.

13. Another example: Subtract ‘1’ from each side Cube each side Add ‘5’ to each side

14. Example: Same thing as: Add ‘2’ to both sides “cube” both sides Subtract “3” from both sides

15. Your Turn: 8. 9. This will be written as: 10.

16. Solve rational equations of Exponent form Isolate the ‘x’ term  divide by ‘2’ 2/3 root  but use exponents to do it How do you “undo” 3/2 power? Convert to radical form to simplify

17. Solve rational equations of Exponent form Isolate the ‘x’ term  divide by ‘9’ 5/3 root  but use exponents to do it How do you “undo” 3/5 power? Convert to radical form to simplify

18. Your Turn: 11. 12.

19. More complicated: Add ‘21’ to both sides Divide both sides by “-2” Need an exponent of ‘1’ on ‘x’  raise both sides to the ¾ power.  raise both sides to the ¾ power. 4 th root of 16 raised to the 3 rd power

20. Your Turn: 13. 14. 15.

21. Vocabulary Extraneous Solution: a solution that, when plugged back into the original equation, plugged back into the original equation, does not make a true statement. does not make a true statement.

22. Get the radical all by itself Square both sides Subtract ‘x’ and ’10’ from both sides. Divide both sides by ‘4’. Non standard form quadratic Equations with two solutions

23. Factor Solve using zero product property Write quadratic in standard form. Check for extranious solutions. Check: x = 3 in the original equation.

24. Check for extraneous solutions. Check: x = 3 ? ? x = 3 is extraneous Check: x = -2 ? ? x = -2 is the only solution ?

25. Your turn: 16. 17.

26. Equations with two radicals (the easy version) Square left/right sides Add 2x left/right Subtract 3 left/right divide 3 left/right

27. Your turn: Solve 18. 19.

28. How would you multiply this out? FOIL

29. Your turn: 20. Simplify the product.

30. Equations with two radicals Since they are not “like” radicals (same radicand and index number) (same radicand and index number) you can’t just combine them. you can’t just combine them. If we got rid of one of the radicals (by squaring it) then we could then solve the equation. it) then we could then solve the equation. Square both sides.

31. Equations with two radicals F.O.I.L. Combine like terms

32. Equations with two radicals Subtract 10 (left/right) Subtract x (left/right) divide by 4 (left/right) Square (left/right) Subtract ‘x’ and ‘6’ (left/right) Factor and solve: x = 3, -2 x = 3, -2 Check the solution

33. Your turn: 21. solve

34. HOMEWORK  Section 6-6  Blog