7.1 N th Roots and Rational Exponents 7.2 Properties of Rational Exponents 7.3 Power Functions and Function Operations 7.4 Inverse Functions 7.5 Graphing Square Root and Cube Root Functions 7.6 Solving Radical Equations Homework Assignments OPENERS EXTRA REVIEW: Domain and Range EXTRA REVIEW: No Calculator EXTRA REVIEW: Ugly Radicals CH 7 Powers Roots Radicals,

7.1 Roots and Rational Exponents EXPONENT RULE #1

CH 7 Powers Roots Radicals 7.1 Roots and Rational Exponents

CH 7 Powers Roots Radicals 7.1 Roots and Rational Exponents

CH 7 Powers Roots Radicals 7.2 Properties of Rational Exponents

CH 7 Powers Roots Radicals 7.2 Properties of Rational Exponents

CH 7 Powers Roots Radicals 7.2 Properties of Rational Exponents

CH 7 Powers Roots Radicals 7.2 Properties of Rational Exponents

CH 7 Powers Roots Radicals 7.2 Properties of Rational Exponents

Practice problems: Simplify each of the following. CH 7 Powers Roots Radicals 7.2 Properties of Rational Exponents

CH 7 Powers Roots Radicals 7.2 Properties of Rational Exponents

CH 7 Powers Roots Radicals 7.2 Properties of Rational Exponents

CH 7 Powers Roots Radicals 7.2 Properties of Rational Exponents

CH 7 Powers Roots Radicals 7.2 Properties of Rational Exponents

CH 7 Powers Roots Radicals 7.2 Properties of Rational Exponents

CH 7 Powers Roots Radicals 7.2 Properties of Rational Exponents

CH 7 Powers Roots Radicals 7.2 Properties of Rational Exponents

CH 7 Powers Roots Radicals 7.2 Properties of Rational Exponents I’m Confused!!! I don’t get this stuff and we have a quiz on it tomorrow!

CH 7 Powers Roots Radicals 7.2 Properties of Rational Exponents

CH 7 Powers Roots Radicals 7.3 Power Functions

CH 7 Powers Roots Radicals 7.3 Power Functions

We can write this as: f(3)+g(3) or f + g (3) or (f + g) (3) CH 7 Powers Roots Radicals 7.3 Power Functions

This means we are going to take the equations (with x still in them) and add them together. CH 7 Powers Roots Radicals 7.3 Power Functions

CH 7 Powers Roots Radicals 7.3 Power Functions

This means we are going to find g(27) Then put that answer into f(x) CH 7 Powers Roots Radicals 7.3 Power Functions

CH 7 Powers Roots Radicals 7.3 Power Functions

OK, this is the hard part. We are going to put an entire equation into the other equation, without putting in a number for x CH 7 Powers Roots Radicals 7.3 Power Functions

CH 7 Powers Roots Radicals 7.3 Power Functions

CH 7 Powers Roots Radicals 7.3 Power Functions

Click for Composite Function Activity Click for Extra Function Practice

CH 7 Powers Roots Radicals 7.3 Power Functions DOMAIN and RANGE: The DOMAIN and RANGE are properties of an equation. They Tell you… …what numbers can go IN to an equation. and …what numbers can come OUT of an equation

DOMAIN RANGE INPUT The numbers we put into the equation are called the The numbers we get out of the equation are called the OUTPUT CH 7 Powers Roots Radicals 7.3 Power Functions

CH 7 Powers Roots Radicals 7.3 Power Functions DOMAIN: The list of all possible inputs for a function. RANGE: The list of all possible outputs for a function.

CH 7 Powers Roots Radicals 7.3 Power Functions DOMAIN: The list of all possible inputs for a function. For many functions, there is no restriction for what we can put into it. If there is no restriction, we say the domain is “ALL REAL NUMBERS” You can put any number you can think of in for x.

CH 7 Powers Roots Radicals 7.3 Power Functions DOMAIN: The list of all possible inputs for a function. There are some functions that do have restrictions. For each of the following problems, there are numbers that we are NOT allowed to use for x. Domain:

CH 7 Powers Roots Radicals 7.3 Power Functions DOMAIN: The list of all possible inputs for a function. Domain:

CH 7 Powers Roots Radicals 7.3 Power Functions DOMAIN: You can use the graph to help identify the domain Domain:

CH 7 Powers Roots Radicals 7.3 Power Functions DOMAIN: You can use the graph to help identify the domain Domain:

CH 7 Powers Roots Radicals 7.3 Power Functions DOMAIN: You can use the graph to help identify the domain Domain:

CH 7 Powers Roots Radicals 7.3 Power Functions RANGE: The list of all possible outputs for a function. RANGE:

CH 7 Powers Roots Radicals 7.3 Power Functions RANGE: The list of all possible outputs for a function. RANGE:

CH 7 Powers Roots Radicals 7.3 Power Functions RANGE: The list of all possible outputs for a function. RANGE:

CH 7 Powers Roots Radicals 7.4 Inverse Functions

CH 7 Powers Roots Radicals 7.4 Inverse Functions

If Then To prove that two functions are inverses… Show that the composite functions cancel out AND CH 7 Powers Roots Radicals 7.4 Inverse Functions

FIND THE INVERSE OF A POWER FUNCTION CH 7 Powers Roots Radicals 7.4 Inverse Functions

IMPORTANT SIDE_NOTE CH 7 Powers Roots Radicals 7.4 Inverse Functions

CH 7 Powers Roots Radicals 7.4 Inverse Functions

CH 7 Powers Roots Radicals 7.4 Inverse Functions

0,7 -8,0 7,0 0,-8 CH 7 Powers Roots Radicals 7.4 Inverse Functions

CH 7 Powers Roots Radicals 7.4 Inverse Functions

CH 7 Powers Roots Radicals 7.4 Inverse Functions

INVERSES CH 7 Powers Roots Radicals 7.3 Power Functions

INVERSES CH 7 Powers Roots Radicals 7.3 Power Functions

NOW FIND THE INVERSE FUNCTION Its like going backwards Switch x and y Resolve for y CH 7 Powers Roots Radicals 7.3 Power Functions

DO YOU KNOW………. How to find the inverse of a function? Verify that 2 functions are inverses? How to identify inverses from their graphs? Tell if an equation and it’s inverse are functions?

CH 7 Powers Roots Radicals 7.5 Square and Cube Root Graphs

CH 7 Powers Roots Radicals 7.5 Square and Cube Root Graphs

CH 7 Powers Roots Radicals 7.5 Square and Cube Root Graphs

CH 7 Powers Roots Radicals 7.5 Square and Cube Root Graphs

CH 7 Powers Roots Radicals 7.5 Square and Cube Root Graphs

CH 7 Powers Roots Radicals 7.5 Square and Cube Root Graphs

X Min: -10 X Max: 10 Y Min: -200 Y Max: 200 CH 7 Powers Roots Radicals 7.5 Square and Cube Root Graphs

CH 7 Powers Roots Radicals 7.5 Square and Cube Root Graphs

CH 7 Powers Roots Radicals 7.5 Square and Cube Root Graphs

CH 7 Powers Roots Radicals 7.5 Square and Cube Root Graphs

CH 7 Powers Roots Radicals 7.5 Square and Cube Root Graphs

CH 7 Powers Roots Radicals 7.5 Square and Cube Root Graphs

CH 7 Powers Roots Radicals 7.5 Square and Cube Root Graphs

CH 7 Powers Roots Radicals 7.5 Square and Cube Root Graphs

CH 7 Powers Roots Radicals 7.5 Square and Cube Root Graphs

CH 7 Powers Roots Radicals 7.5 Square and Cube Root Graphs

CH 7 Powers Roots Radicals 7.5 Square and Cube Root Graphs

CH 7 Powers Roots Radicals 7.5 Square and Cube Root Graphs

CH 7 Powers Roots Radicals 7.6 Solve Radical Equations

CH 7 Powers Roots Radicals Homework Homework Assignments: Worksheet 7.1 p. 411 Pamphlet p. 418 p. 426 p. 441

A A B C D E F G H I J K L M N OBCDEFGHI JKLMNO CH 7 Powers Roots Radicals OPENERS

1 CH 7 Powers Roots Radicals OPENERS A

1 CH 7 Powers Roots Radicals OPENERS B

The population of Utah grows at a rate of Where y is the population, and x is the year. In what year was the population 308,268? CH 7 Powers Roots Radicals OPENERS C

1 CH 7 Powers Roots Radicals OPENERS D

1 CH 7 Powers Roots Radicals OPENERS E

1 CH 7 Powers Roots Radicals OPENERS F

1 CH 7 Powers Roots Radicals OPENERS G

1 CH 7 Powers Roots Radicals OPENERS H

1 CH 7 Powers Roots Radicals OPENERS I

1 CH 7 Powers Roots Radicals OPENERS J

1 CH 7 Powers Roots Radicals OPENERS K

CH 7 Powers Roots Radicals OPENERS L

CH 7 Powers Roots Radicals OPENERS M

CH 7 Powers Roots Radicals OPENERS N

State the domain for each of the following: CH 7 Powers Roots Radicals Extra Review Domain and Range R R R R R R R R R R How does Domain always start ? Which problems have the fraction restriction? Which problems have the even root restriction?

State the range for each of the following: CH 7 Powers Roots Radicals Extra Review Domain and Range How do we start? For range, we only discussed the restriction when taking even roots. R R RR R R R R

State the range for each of the following: CH 7 Powers Roots Radicals Extra Review: No Calc

State the range for each of the following: 1.2. CH 7 Powers Roots Radicals Extra Review: Ugly Radicals

State the range for each of the following: 3. CH 7 Powers Roots Radicals Extra Review: Ugly Radicals