Algebra-2 Section 6-6 Solve Radical Functions

Quiz 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

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

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.

Your turn: 4. What is the domain of the function? 5. What is the transformation to the parent function that is represented below? that is represented below?

What is the difference between the following two equations?

Commutative Property: Is there a better way to write this to avoid confusion?

Your turn: 6. What is the transformation to the parent function (square root function) that is represented by the following?

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.” = 3x 12 = 3x ÷ 3 4 = x

Remember “Isolate the square, Undo the square” ? “undo” really means use the inverse of the function “undo” an exponent really means use power of a power with the inverse of exponent

“isolate the square, undo the square” ÷2 ÷2 Isolate the base and its exponent. exponent. “undo” squaring Use the inverse of the square function. Even Root !!!  ± result x = 6, 2 Do the math!!!

“Isolate the square, undo the square” ÷2÷2 Isolate the base and its exponent. exponent. “undo” squaring Use the inverse of exponent 2. Even Root !!!  ± result x = 6, 2 Do the math!!!

Your Turn: Solve for ‘x’ 7. 8.

“isolate the radical, undo the radical” Remove the radical by using the inverse function (of a square root) x = 3 Isolate ‘x’ on one side of the equal sign by subtracting 6 from both sides. Square and square root are inverse functions of each other. Check your answer! Checks!

“Isolate the radical, undo the radical” Subtract ‘1’ from each side Cube each side Add ‘5’ to each side Check your answer! Checks! Substitute the solution into the original equation.

Your Turn: Solve for ‘x’

“Isolate the radical, undo the radical” Add ‘2’ to both sides “cube” both sides Subtract “3” from both sides Check the solution Solution checks!

Your Turn: 11.

12.

13.

“Isolate the power, undo the power” Isolate the ‘x’ term  divide by ‘9’ 5/3 root  but use exponents to do it How do you “undo” 3/5 power? ⅓ root of 8, then the 5 th power of the result) Or, use the calculator

“Isolate the power, undo the power” Check your solution. Use your calculator. Solution checks!

Your Turn: 14. Solution checks

Your Turn: 15. Checks

16.

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.

Isolate the Radical, undo the radical 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

Solve by factoring Solve using zero product property Write quadratic in standard form. Check for extranious solutions. Check: x = 3? x = 3 is extraneous

? ? Check: x = -2 ? ? x = -2 is the only solution

Your turn: 17. x = -3 is extraneous x = 12 is a solution.

Your turn: 18. Check x = 6 Only one solution! Check x = 1 x = 1 is extraneous x = 1 is extraneous

Equations with two radicals Square left/right Square both sides.

Your turn: 19. Check x = 1