6-2 Study Guide and Intervention - Parallelograms
Chapter 6. 11. Glencoe Geometry. 6-2 Study Guide and Intervention. Parallelograms. Sides and Angles of Parallelograms A quadrilateral with.
6-2 Study Guide and Intervention - Substitution
Chapter 6. 12. Glencoe Algebra 1. 6-2 Study Guide and Intervention. Substitution. Solve by Substitution One method of solving systems of equations is
6-2 Study Guide and Intervention
6-2 Study Guide and Intervention. Substitution. Solve by Substitution One method of solving systems of equations is substitution.
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angles of those n - 2 triangles. Polygon Interior Angle. Sum Theorem 2. 6-3 Study Guide and Intervention. Tests for Parallelograms.
2-6 - Study Guide and Intervention
Substitution Property of Equality. Exercises. Complete each proof. Study Guide and Intervention. Algebraic Proof. 2-6. Example. 2. Given: 4x + 8 = x + 2.
6-1 Study Guide and Intervention
The solution of the system is x = –1 y = 1
6-2 Study Guide and Intervention
Chapter 6. 12. Glencoe Algebra 2. Inverse Relations Find Inverses. Find the inverse of the function f(1) = 2 ... 6-2 Study Guide and Intervention.
5-2 - Study Guide and Intervention
Lesson 5-2. PDF Pass. Chapter 5. 11. Glencoe Algebra 2. Study Guide and Intervention. Dividing Polynomials. 5-2. Long Division To divide a polynomial by a
5-1 Study Guide and Intervention
2. ). 5. If cot ? = –. 4. 3 and sin ? < 0 find cos ? and csc ?. 6. 6. Glencoe Precalculus. 5-1 Study Guide and Intervention(continued).
5-2 Study Guide and Intervention.pdf
5-2 Study Guide and Intervention. Solving Inequalities by Multiplication and Division. NAME. Multiplication Property of Inequalities.
6-2 Study Guide and Intervention - The Masters Program
6-2 Study Guide and Intervention (continued) Parallelograms Diagonals of ParallelogramsTwo important properties of parallelograms deal with their diagonals If ABCD is a parallelogram then If a quadrilateral is a parallelogram then its diagonals bisect each other AP = PC and DP = PB
(PDF) Study Guide and Intervention Workbook ISAIAH HEILMAN -
6-2 Study Guide and Intervention Substitution Solve by Substitution One method of solving systems of equations is substitution Example 1: Use substitution to solve the system of Example 2: Solve for one variable equations then substitute y = 2x 4x – y = –4 Substitute 2x x + 3y = 7 2x – 4y = –6 for 4x – y = –4
6-2 Study Guide and Intervention - Central Dauphin School
Title: Chapter 6 Resource Masters Author: Glencoe/McGraw-Hill Subject: Glencoe Geometry Created Date: 12/10/2014 9:30:50 PM
2-6 Study Guide and Intervention - Ms Wallenberg's Math Site
Chapter 2 36 Glencoe Algebra 2 2-6 Study Guide and Intervention Special Functions Piecewise-Defined Functions A piecewise-defined function is written using two
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Study Guide and Intervention (continued) Inverse Functions and Relations Example 1 Example 2 yes no no no yes yes yes no yes yes yes 011_020_ALG2_A_CRM_C06_CR_660551
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Chapter 6 12 Glencoe Algebra 2
Inverse RelationsTwo relations are inverse relations if and only if whenever one relation contains the
element ( a , b), the other relation contains the element (b, a).Property of Inverse
FunctionsSuppose f and f
1 are inverse functions.Then f(a) = b if and only if f
1 b ) = a.Find Inverses
Find the inverse of the function f(x) =
2 5 x 1 5 . Then graph the function and its inverse. Step 1 Replace f(x) with y in the original equation. f(x) = 2 5 x - 1 5 → y = 2 5 x - 1 5Step 2 Interchange x and y.
x = 2 5 y - 1 5Step 3 Solve for y.
x = 2 5 y - 1 5Inverse of y =
2 5 x - 1 55x = 2y - 1
Multiply each side by 5.
5x + 1 = 2y Add 1 to each side.
12 ( 5x + 1) = y Divide each side by 2.
The inverse of
f(x) = 2 5 x - 1 5 is f 1 x 1 2 (5x + 1).Exercises
Find the inverse of each function. Then graph the function and its inverse.1. f(x) =
2 3 x - 1 2. f(x) = 2x - 3 3. f(x) = 1 4 x - 2xO f(x) = 2-5 x 1-5 242 2 2 4 4
4f(x)f
-1 x 5-2 x 1-2 xO f 1 x 1-2 x 3-2 f x 2 x 3 f(x) 244 2 2 4 -4xO f x 2-3 x 1 f -1 x 3-2 x 3- 2 f(x) 24
4 2 2 4 -4 xO f(x) = 1-4 x - 2 f 1 x 4 x 8 f(x) 24
2 4 2 2 4 -4
6-2Study Guide and Intervention
Inverse Functions and Relations
Example
f 1 x) = 3 2 x + 3 2 f 1 x) = 1 2 x + 3 2 f 1 x) = 4x + 8011_020_ALG2_A_CRM_C06_CR_660551.indd 12
011_020_ALG2_A_CRM_C06_CR_660551.indd 1212/20/10 9:20 PM12/20/10 9:20 PM
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Lesson 6-2
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Chapter 6 13 Glencoe Algebra 2
6-2Verifying Inverses
Determine whether f(x) = 2x - 7 and g(x) =
1 2 (x + 7) are inverse functions. [f g](x) = f[g(x)] [g f](x) = g[f(x)] f 1 2 (x + 7) = g(2x - 7) 2 1 2 (x + 7) - 7 = 1 2 (2x - 7 + 7) x + 7 - 7 = x xThe functions are inverses since both [f
g](x) = x and [g f](x) = x.Determine whether f(x) = 4x +
1 3 and g(x) = 1 4 x - 3 are inverse functions. [f g](x) = f[g(x)] = f 1 4 x - 3 4 1 4 x - 3 1 3 = x - 12 + 1 3 = x - 11 2 3Since [f
g](x) ≠ x, the functions are not inverses.Exercises
Determine whether each pair of functions are inverse functions. Write yes or no.1. f(x) = 3x - 1 2. f(x) =
1 4 x + 5 3. f(x) = 1 2 x - 10 g(x) = 1 3 x + 1 3 g(x) = 4x - 20 g(x) = 2x + 1 104. f(x) = 2x + 5 5. f(x) = 8x - 12 6. f(x) = -2x + 3
g(x) = 5x + 2 g(x) = 1 8 x + 12 g(x) = - 1 2 x + 3 27. f(x) = 4x -
1 28. f(x) = 2x -
3 59. f(x) = 4x +
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