Download Algebra 2 Unit 4 Notebook Guide

Name:________________________
Algebra 2
Unit 4
Notebook Guide
Unit Topic: Rational Exponents and Radical Functions (Chapter 6)
Date
Lesson
Textbook Section Homework Assignment
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1. Evaluate nth Roots and Use Rational Exponents 6.1 HW #1 (p. 417) 7, 9, 11, 13, 21, 23, 25, 27, 29, 31, 51, 53
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2. Apply Properties of Rational Exponents
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3. Perform Function Operations and Composition 6.3 HW #3 (p. 432) 3, 7, 13, 17, 23, 25, 29, 35, [41]
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4. Use Inverse Functions
6.4 HW #4 (p. 442) 3, 7, 11, 17, 19, 25, 27, 39, [41, 45]
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5. Graph Square Root and Cube Root Functions
6.5 HW #5 (p. 449) 3, 7, 11, 17, 21, 29, 31, 33, [40]
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6. Solve Radical Equations
6.6 HW #6 (p. 456) 3, 5, 13, 15, 23, 25, 35, 37, [47, 53]
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7. Skills Review
HW #7 (p. 424) 9, 21, 31, 39, 47, 53, [68]
and (p. 456) 9, 17, 29, 41, [51, 54]
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8. Unit 4 Review
Unit 4 Review
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9. Problem Solving
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6.2 HW #2 (p. 424) 5, 7, 17, 19, 27, 29, 35, 37, 45, 55, [67]
6.1-6.6 Problem Solving (p. 436) 1, 2 (p. 464) 4, 9
10. Unit 4 Test
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Note: Please label your homework assignment as shown above along with your name.
Grade Tracking
Homework Quiz #1
/6
Homework Quiz #2
/6
Homework Quiz #3
/6
Problem Solving
/12
Unit Test
/100
Points Earned
/130
Unit Average (w/o bumps) ______
Homework Bumps
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Unit Average (w/ bumps)
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Prior Unit Averages
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Cumulative Average
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IXL Assignments: L.13 and M.5 are mandatory. Practice any other skills in sections L or M as needed.
Algebra 2 Concepts - Unit 4 (textbook sections 6.1 – 6.6)
The nth root of a number is a factor that produces the number in question when repeated n times.
For example, 3 is a 4th root of 81, because 3∙3∙3∙3, or 34, results in a product of 81. You can verify
that −3, 3i, and −3i are also 4th roots of 81 by calculating (−3)4, (3i)4, and (−3i)4, all of which
produce 81. To generalize, we can say that every complex number has two square roots, three cube
roots, four 4th roots, five 5th roots, etc. However, when using only real numbers, we find that
positive reals have a positive/negative pair of square roots, 4th roots, etc., and a single 3rd root, 5th
root, etc.; and that negative reals have no even roots and single odd roots.
A composition of functions is the linking together of two or more of functions such that the output
from one function becomes the input to the next function. To say that “h of x” is a composite
function equal to “f of g of x”, we write h(x) = f(g(x)) (or h(x) = (f ◦ g)(x) may be used), indicating
that x is the input to function g, and the output of g is the input to function f. In general, f(g(x)) is
not equal to g(f(x)), which is to say the order in which functions are composed will affect the result.
The inverse of a function is a function that undoes another function. If an input x into a function f
results in an output y, then putting y into the inverse function f −1 (read “f inverse”) results in x. The
composition of a function and its inverse will therefore have an output equal to the input, and this is
true regardless of the order of composition; or equivalently, f(f −1(x)) = x and f −1(f(x)) = x.
Graphically, a function and its inverse will be reflections of one another across the line y = x.
Because this reflection changes a horizontal line into a vertical line, any function that does not pass
the horizontal line test has an inverse that is not a function because the reflection does not pass the
vertical line test.
An extraneous solution is a solution to an equation that emerges from the algebraic process of
solving the equation but is not a valid solution to the original equation. By checking solutions in
the original equation, or by graphing each side of the original equation and finding the intersection
points, you can verify whether a solution is valid or extraneous.