Algebra 3 Chapter 7: Powers, Roots, and Radicals Lesson 3: Power
advertisement
Warm Up οSolve 3 ο1. 5(π₯ − 1) ο2. π₯ − 3 + (π₯ 2 − 1) 2 ο3. π₯ + 2 − (π₯ − 1) ο4. π₯−3 π₯+2 2 ο5. (π₯ − 4) Algebra 3 Chapter 7: Powers, Roots, and Radicals Lesson 3: Power Functions and Function Operations VOCAB οPower Function – an equation in π the form π¦ = ππ₯ οComposition – is when the domain of the function H is the set of all x values such that x is in the domain of g and g(x) is in the domain of f. β π₯ = π(π π₯ ) TODAY οToday we will learn how to combine 2 or more functions using basic operations. Directions (Operations on Functions) οAddition – Combine like terms οSubtraction - Combine like terms οMultiplication – Distribute / FOIL οDivision – Long / Synthetic ο+- Powers don’t change ο* Powers add οDivision Powers subtract οSolve I DO (Basic operations) 2 π π₯ = 3π₯ 3 ο1. π π₯ + π(π₯) ο2. π π₯ − π(π₯) οSolve π π₯ = 7π₯ ο3. π π₯ ∗ π(π₯) ο4. π π₯ π(π₯) and π π₯ = −5π₯ and π π₯ = 2π₯ 3 4 2 3 οSolve WE DO (Basic operations) 2 π π₯ = 2π₯ − 7π₯ + 13 π π₯ = π₯2 − 6 ο1. π π₯ + π(π₯) ο2. g π₯ − π(π₯) οSolve π π₯ = −3π₯ ο3. π π₯ ∗ π(π₯) ο4. π π₯ π(π₯) 1 4 and and π π₯ = 9π₯ 1 2 YOU DO 2(Basic operations) οSolve π₯2 + 7 π π₯ = π₯ + 12π₯ and π π₯ = ο1. π π₯ + π(π₯) ο2. g π₯ − π(π₯) οSolve π π₯ = 5π₯ ο3. π π₯ ∗ π(π₯) ο4. π π₯ π(π₯) 4 5 and π π₯ = 10π₯ 1 3 Review οToday you learned how to combine more than one equation HOMEWORK οWorksheet ο7.3B (1 – 8) ο7 & 8 – do division as well Warm Up οSolve π π₯ = 2π₯ 2 + 2 and π π₯ = π₯ 2 − 7π₯ ο1. π π₯ + π(π₯) ο2. g π₯ − π(π₯) οSolve π π₯ = −6π₯ ο3. π π₯ ∗ π(π₯) ο4. π π₯ π(π₯) 3 5 and π π₯ = 24π₯ 1 3 Algebra 3 Chapter 7: Powers, Roots, and Radicals Lesson 3: Power Functions and Function Operations TODAY οToday we will review long and synthetic division (combining 2 equations) Question ο When can I use synthetic division? Directions (Synthetic) ο THIS IS EXACTLY LIKE SYNTHETIC SUBSTITUTION ο Write the problem in standard form including the missing terms ο Only Write down the coefficients inside ο For the outside ο Remember to take the opposite of the number ο ANSWER ο YOU start with 1 power less than the original Directions (Long Division) ο THIS IS EXACTLY LIKE LONG DIVISION WITHOUT A CALCULATOR ο Write the problem in standard form including the missing terms ο Look at the first term in the divisor ο Find how many times that goes into the first term of the polynomial ο Multiply that answer times the WHOLE divisor ο Subtract that from the polynomial ο Keep going until you can’t do anymore ο Remainder is then written over the divisor STARTING POINT ο Lets take a look at a basic division problem without a calculator 2136 ο 35 I DO (Division) ο Divide ο 1. π ο 2. π ο 3. π ο 4. π π₯ π₯ π₯ π₯ the functions = −π₯ 2 + 2π₯ + 2 = 2π₯ =π₯−2 =π₯+1 π(π₯) π(π₯) π π π π π₯ π₯ π₯ π₯ =π₯+3 =π₯+5 = π₯2 + π₯ − 4 = 3π₯ − 2 WE DO (Division) ο Divide ο 1. the functions π(π₯) π(π₯) π π₯ = π₯2 + 1 π π₯ ο 2. π π₯ = 2π₯ 3 − 3π₯ + 4 π π₯ ο 3. π π₯ = 2π₯ 4 + 3π₯ 3 + 5π₯ − 1 π π₯ ο 4. π π₯ = π₯ 3 − 3π₯ 2 + 2π₯ − 6 π π₯ =π₯−2 =π₯−1 = π₯ 2 − 2π₯ + 2 = π₯ 2 + 3π₯ − 1 YOU DO (Division) ο Divide ο 1. the functions π(π₯) π(π₯) π π₯ = −π₯ 2 + 2π₯ + 2 π π₯ ο 2. π π₯ = 4π₯ 3 − 2π₯ 2 + 1 π π₯ ο 3. π π₯ = 4π₯ 3 − 2π₯ 2 + 6π₯ − 1 π π₯ ο 4. π π₯ = 2π₯ 4 + 3π₯ − 1 π π₯ =π₯+3 =π₯+2 = 2π₯ + 3 = π₯ 2 + 2π₯ + 1 Review ο Today you learned……… HOMEWORK οWorksheet ο7.3B (9-12) Warm Up οSolve 3 ο1. 7(π₯ − 2) ο2. π₯ + 3 + (π₯ 2 − 1) 2 ο3. π₯ + 3 − (π₯ − 1) ο4. π₯+3 π₯−2 2 ο5. (π₯ − 3) Algebra 3 Chapter 7: Powers, Roots, and Radicals Lesson 3: Power Functions and Function Operations TODAY οToday we will learn how to find a composite of 2 functions. Directions (Compositions) ο Work inside out ο Write ο This ο Write down the inside function is the X of the outside function down the outside function (while using what you wrote as x) ο Simplify I DO (Composition) ο Find the composite of the given functions π π₯ = 10π₯ π π₯ =π₯+4 ο 1. ο 2. π π π₯ π(π π₯ ) ο 3. π(π π₯ ) ο 4. π(π π₯ ) WE DO (Composition) ο Find the composite of the given functions π π₯ = 3π₯ 2 π π₯ = 2π₯ − 1 ο 1. ο 2. π π π₯ π(π π₯ ) ο 3. π(π π₯ ) ο 4. π(π π₯ ) YOU DO (Composition) ο Find the composite of the given functions π π₯ = 2π₯ 2 + 1 π π₯ = 3π₯ + 4 ο 1. ο 2. π π π₯ π(π π₯ ) ο 3. π(π π₯ ) ο 4. π(π π₯ ) Review ο Today you learned……… HOMEWORK οWorksheet ο7.3B (13-16) Warm Up οFind the composite of the given functions 2 π π₯ = 2π₯ − 4 π π₯ = 3π₯ − 2 ο1. π π π₯ ο2. π(π π₯ ) Algebra 3 Chapter 7: Powers, Roots, and Radicals Lesson 3: Power Functions and Function Operations TODAY οToday we will learn how to find a composite of 2 functions with negative and fraction exponents. Directions (Compositions) ο Work inside out ο Write ο This ο Write down the inside function is the X of the outside function down the outside function (while using what you wrote as x) ο Simplify I DO (Composition) ο Find the composite of the given functions π π₯ = 3π₯ ο 1. ο 2. π π π₯ π(π π₯ ) ο 3. π(π π₯ ) ο 4. π(π π₯ ) 1 3 2 3 π π₯ =π₯ +1 WE DO (Composition) ο Find the composite of the given functions π π₯ = 3π₯ −1 π π₯ = 2π₯ − 1 ο 1. ο 2. π π π₯ π(π π₯ ) ο 3. π(π π₯ ) ο 4. π(π π₯ ) YOU DO (Composition) ο Find the composite of the given functions 1 4 π π₯ = 2π₯ − 1 ο 1. ο 2. π π π₯ π(π π₯ ) ο 3. π(π π₯ ) ο 4. π(π π₯ ) 2 3 π π₯ =π₯ +2 Review ο Today you learned……… HOMEWORK οWorksheet ο7.3B (13-16)
