Chapter+7

The following are the roles of our group's wiki: NOTE FROM MRS. KEENER: Point values have increased by 10 points in the rubric. Meaning the most points achievable is 25 due to the time to make a video and embed it. All group members must participate in the video in some way. You are required to post how you contributed to the video below this information. **I contributed to the video by being in the video and coming up with some of the ideas for the clips. :)Kourtneyyy i contributed to the video by being in it and helping to put together the clips for the final video on imovie, john I contributed to the video by being in the vidwo and filming it as well. In addition to planning some of the action and all that good stuff, zach** I contributed to the video by being in it. Jasmine I Contributed By Filming Part Of The Video And Was In The Beginning. Chris =Chapter 7 Wiki: Powers, Roots, and Radicals = roots radicals || how to use rational exponets and nth roots of numbers how to perform operations with and find inverses of functions how to graph radical functions and solve radical equations ||  __Key Vocabulary__ Section 7.1: //n //th Roots and Rational Exponents media type="youtube" key="wDn8IuAgRwc" height="344" width="425" Evaluate nth rooth. Using Nth roots in real life.
 * __**Roles of Wiki**__ || __**Student**__ ||
 * **Editor** || C. Maskaly ||
 * **Multimedia** || K. Frey ||
 * **Text** || Z. Wooten ||
 * **Practice Problems** || J. Stone ||
 * **Career/Real Life App** || J. Scott ||
 * **What is this chapter about? ** || **What will you learn? ** ||
 * powers
 * nth root of a** (p. 401) For an integer //n// greater than 1, if b^n = a, then b is an nth root of a.
 * index** (p. 401) The integer //n// (greater than 1) in the expression the nth root of a.
 * simplest form** (p. 408) a radical expression after you apply the properties of radicals, remove any perfect nth powers, and rationalize any denominators)
 * like radicals** (p. 408) Two radical expressions that have the same index and the same radicand.**power function** (p. 415) A function of the form y = ax^b where a is a real number and b is a rational number.
 * composition** (p. 416) The composition of the function f with the function g is h(x) - f(g)(x)).
 * inverse relation** (p. 422) A relation that maps the output values of an original relation back to their original input values. The graph of an inverse relation is the reflection of the graph of the original relation.
 * inverse function** (p. 422) A relation and its inverse relation whenever both relations are functions.
 * radical functions** (p. 431) A function that contains a radical, such as y = the square root of x or y = the cubic root of x.

You can extend the concept of a square root to other types of roots. If b is > 1, and b^n = a, then b is the nth root of a.

Real Nth Roots - If n is odd then a has one real nth root. - If n is even and positive then it has two real nth roots. - If n is even and = 0 then it has one nth root. - If n is even and a < 0, then a has no real nth roots.


 * practice:Evaulate-9^3/2, answer on pg. 401

<span style="color: rgb(38, 38, 237);">Section 7.2: Properties of Rational Exponents Properties of Rational Exponets and Radicals. The properties of integer exponets can be applied to rational exponets. (See chart on page 407).
 * <span style="color: rgb(38, 38, 237);">practice:Simplify- (8^1/2 x 5^1/3)^2, answer on pg. 407

<span style="color: rgb(229, 16, 16);">Section 7.3: Power Functions and Function Operations Performing function operations. Using Function Operations in Real Life.
 * <span style="color: rgb(229, 16, 16);">practice:Let f(x)=3x-1 and g(x)=2x-1, find f(f(x)), answer on pg. 416

<span style="color: rgb(244, 123, 21);">Section 7.4: Inverse Functions Finding Inverses of Linear Functions.
 * <span style="color: rgb(244, 123, 21);">practice:Find the inverse of y=2x-4, answer on pg. 422

<span style="color: rgb(255, 0, 255);">Section 7.5: Graphing Square Root and Cube Root Functions Graphing Radical functions. Using Radical Functions in Real Life.
 * <span style="color: rgb(255, 0, 255);">practice:Describe how to obtain the graph of y= (x+1)^1/2)-3 from the graph of x^1/2, answer on pg. 432

<span style="color: rgb(66, 237, 38);">
> It can be a person, or a dog, or anything you want. Just speak and explain out loud using your own words. > Your understanding will improve dramatically.
 * <span style="color: rgb(66, 237, 38);">Go back and re-read your notes.
 * <span style="color: rgb(66, 237, 38);">Study this wiki and try the practice problems.
 * <span style="color: rgb(66, 237, 38);">Try some odds.
 * <span style="color: rgb(66, 237, 38);">Do the review on page 456 and the test following it.
 * <span style="color: rgb(66, 237, 38);">Look over your 7.1-7.4 test.
 * <span style="color: rgb(66, 237, 38);">Go through everything we've learned this unit, and TEACH it to someone else.
 * <span style="color: rgb(66, 237, 38);">Go ask Mrs. Keener for help during her free lunch periods.

=__<span style="color: rgb(255, 0, 0);">REMEMBER THE TEST IS THIS FRIDAY! GOOD LUCK! __=

media type="file" key="wikispace video.mov"

<span style="color: rgb(128, 0, 128);">Section 7.6: Solving Radical Equations practice:Solve x^1/3)-4=0, answer on pg. 437

Section 7.7: Statistics and Statistical Graphs practice:What is the symbol for sigma?, answer on pg.446

<span style="color: rgb(83, 184, 238);"><span style="font-family: Arial,Helvetica,sans-serif;">__<span style="font-size: 120%; font-family: 'Arial Black',Gadget,sans-serif;">Real Life Application Problem: __ 1.) Jake imports furniture from Mexico. The exchange rate is 11.30 pesos per U.S dollar. The cost of each piece of furniture is given in pesos. The total cost of each piece of furniture includes a 15% service charge. A-- Write a function for the total cost in U.S dollars. B-- Write a function for the cost in dollars based on the cost in pesos. (answers given at the bottom)

2.) Radium-226 is a form of radioactive element that decays over time. An inital sample of radium-226 has a mass of 500mg. The mass of radium-226 remaining from the initial sample after "t" years is given by 500 (2 X t/1600). To the nearest miligram, how much radium-226 would be left after 800 years? (answers given at the bottom)

REAL LIFE APPLICATION PROBLEM ASWERS:

1.) A-- P(c) = c + 0.15c B-- D(c) = c/11.30 = 1.15c

2.) 500 (2 - 800/1600) = 500 (2 ^ - .5) = 500 ( 1/2.5) = 500/ 2.5 ~ 354