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6.6 F UNCTION O PERATIONS 6.7 I NVERSE R ELATIONS AND F UNCTIONS Algebra II w/ trig
I. Operations on Functions A. Sum: B. Difference: C. Product: D. Quotient:
II. Find the sum, difference, product, and quotient: A.
III. A. B. Composition of Functions Means: Evaluate g(x) first, then use g(x) as the input for f. Means: Evaluate f(x) first, then use f(x) as the input for g.
IV. Let f(x) = x – 5 and g(x) = x 2 A. (f °g)(-3)B. (f °g)(2) C. (g ° f)(-3)D. (g ° f)(2)
6.7 Inverse Relations and Functions
I. Find the inverse function and graph the function and its inverse. A. f(x) = x + 3 - rewrite f(x) as y - interchange x and y - solve for y - rewrite y as f -1
B. f(x)= 2 / 3 x – 1 C. f(x) = 2x – 3 D. f(x) = 2x + 1 3
Homework Pre-AP p. 401-403 # 9-77 Every other odd p. 410-411 #9-61 Every other odd
7.7 Operations with Functions 7.8 Inverse of Functions Algebra II w/ trig.
13.7 I NVERSE T RIGONOMETRIC F UNCTIONS Algebra II w/ trig.
I.1 ii.2 iii.3 iv.4 1+1=. i.1 ii.2 iii.3 iv.4 1+1=
5.5 Evaluating Logarithms 3/6/2013. Properties of Logarithms Let m and n be positive numbers and b ≠ 1, Product Property Quotient Property Power Property.
Algebra Recap Solve the following equations (i) 3x + 7 = x (ii) 3x + 1 = 5x – 13 (iii) 3(5x – 2) = 4(3x + 6) (iv) 3(2x + 1) = 2x + 11 (v) 2(x + 2)
Operations with Functions Objective: Perform operations with functions and find the composition of two functions.
Algebra II - Chapter /10.2 Logarithms and Functions.
Notes P.5 – Solving Equations. I. Graphically: Ex.- Solve graphically, using two different methods. Solution – See graphing Calculator Overhead.
1.3 EVALUATING LIMITS ANALYTICALLY. Direct Substitution If the the value of c is contained in the domain (the function exists at c) then Direct Substitution.
3.4 Inverse Functions & Relations. Inverse Relations Two relations are inverses if and only if one relation contains the element (b, a) whenever the other.
1 The Chain Rule Section After this lesson, you should be able to: Find the derivative of a composite function using the Chain Rule. Find the derivative.
Agenda Lesson: Solving Multi-Step Inequalities Homework Time.
Algebra II w/trig. Logarithmic expressions can be rewritten using the properties of logarithms. Product Property: the log of a product is the sum of the.
5.5 Double Angle Formulas I. Double Angle Formulas. A) B) C)
4.6 Other Inverse Trig Functions. To get the graphs of the other inverse trig functions we make similar efforts we did to get inverse sine & cosine. We.
7-6 Function Operations Objective 2.01 Use the composition and inverse of functions to model and solve problems; justify results.
Algebra II 7-4 Notes. Inverses In section 2-1 we learned that a relation is a mapping of input values onto output values. An _______ __________ maps.
6.3 BINOMIAL RADICAL EXPRESSIONS Algebra II w/ trig.
Properties of Logarithmic Functions Objective: Simplify and evaluate expressions involving logarithms.
Do Now: Find f(g(x)) and g(f(x)). f(x) = x + 4, g(x) = x f(x) = x + 4, g(x) = x
6.1 ROOTS AND R ADICAL E XPRESSIONS 6.2 M ULTIPLYING AND D IVIDING R ADICAL E XPRESSIONS Algebra II w/ trig.
5.1 M ONOMIALS 5.2 POLYNOMIALS 7.7 O PERATIONS WITH FUNCTIONS Algebra II w/ trig.
Do Now: Evaluate: 3AB. Algebra II 3.7: Evaluate Determinants HW: p.207 (4-14 even) Test : Friday, 12/6.
Algebra I Chapter 3 Warm-ups. Section 3-1 Part I Warm-up USE 2 BOXES! Solve the following equations 1)8x + 7 = 5x )4(3x – 2) = 8(2x + 3) 3) 4) 3(x.
Goals Evaluate and graph log functions. 1Algebra 2 Honors.
Algebra 2 Notes May 4, Graph the following equation: What equation is that log function an inverse of? ◦ Step 1: Use a table to graph the exponential.
Given any function, f, the inverse of the function, f -1, is a relation that is formed by interchanging each (x, y) of f to a (y, x) of f -1.
SFM Productions Presents: Another saga in your continuing Pre-Calculus experience! 1.9Inverse Functions.
Warm-up Find the quotient Section 6-4: Solving Polynomial Equations by Factoring Goal 1.03: Operate with algebraic expressions (polynomial,
5.5Logarithms Objectives: I will be able to… Rewrite equations between exponential and logarithmic forms Evaluate logarithms Solve logarithms.
Solving for (3 Ways). Examples Without using a calculator, what angle(s) would satisfy the equation ?
Derivatives of Trig Functions Objective: Memorize the derivatives of the six trig functions.
~ Chapter 7 ~ Systems of Equations & Inequalities Algebra I Lesson 7-1 Solving Systems by Graphing Lesson 7-2 Solving Systems Using Substitution Lesson.
Homework Questions. Section 4.2 Mrs. Ramsey.
● A variable is a letter which represents an unknown number. Any letter can be used as a variable. ● An algebraic expression contains at least one variable.
Algebra II w/trig. A logarithm is another way to write an exponential. A log is the inverse of an exponential. Definition of Log function: The logarithmic.
4012 u-du : Integrating Composite Functions AP Calculus.
1 Solve each: 1. 5x – 7 > 8x |x – 5| < 2 3. x 2 – 9 > 0 :
Algebra II Honors Problem of the Day Homework: p odds Without graphing find all symmetries for each equation.
Techniques of Differentiation. I. Positive Integer Powers, Multiples, Sums, and Differences A.) Th: If f(x) is a constant, B.) Th: The Power Rule: If.
Derivatives of Logarithmic Functions Objective: Obtain derivative formulas for logs.
In this section, you will learn to: Use standard algebraic techniques to solve trigonometric equations Solve trigonometric equations of quadratic type.
Chapter 2: Functions and Graphs Please review this lecture (from MATH 1100 class) before you begin the section 5.7 (Inverse Trigonometric functions) Copyright.
Roots of Complex Numbers Sec. 6.6c HW: p odd.
Review of 1.4 (Graphing) Compare the graph with.
6.8 G RAPHING R ADICAL F UNCTIONS Algebra II w/ trig.
7.1 and 7.2 Graphing Inequalities 7.3 Solving Equations Using Quadratic Techniques Algebra II w/ trig.
Combinations of Functions Composite Functions. Sum, Difference, Product, and Quotient of Functions Let f and g be two functions with overlapping domains.
Algebra II H Problem of the Day Homework p eoo Sketch the graphs of the following functions. Use a separate graph for each function. Hint: To.
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