Algebra 2 and Trigonometry Chapter 7: Exponential Functions Name: Teacher: Pd: 1
Table of Contents Day 1: Chapter 7-1/7-2: Laws of Exponents SWBAT: Simplify positive, negative, and zero exponents. Pgs. 3 5 in Packet HW: Page 289 # s 3 25 odd Pages 292 293 # s 3 9 odd, 17, 18, 19, 22, 30, 32, 35 75 eoo Day 2: Chapter 7-3: Rational Exponents SWBAT: simplify rational exponents. HW: Pgs. 6 10 in Packet Pages 296 298 # s 3, 5, 6, 18, 19, 22, 32, 39 81 eoo Day 3: Chapter 7-4: Exponential Functions SWBAT: Graph Exponential Functions Pgs. 11 15 in Packet HW: Pages 302 303 # s 3, 4, 7-9 QUIZ Day 4: Chapter 7-5: Exponential Equations SWBAT: Solve Exponential Equations Pgs. 16 18 in Packet HW: Page 305 # s 1-19 odd, 12, 23 Day 5: Chapter 7-6: Exponential Equations SWBAT: Solve Exponential Equations with like and unlike bases Pgs. 19 23 in Packet HW: Pages 307-308 # s 3, 8, 9, 10, 15 35 odd Day 6: Review SWBAT: Solve Problems involving Exponents Pgs. 24 27 in Packet HW: Finish this section in the packet HOMEWORK ANSWER KEYS STARTS AT PAGE 28 2
Day 1: Laws of Exponents SWBAT: Simplify positive, negative, and zero exponents. Warm Up: Exponent Rules Multiplication: Ex. x 2 x 5 = Division: = Ex. = Raising to a Power: (x a ) b = x ab Ex. (x 5 ) 3 = Power of a Product: (xy) a = x a y a Ex. ( ) 3 = Power of a Quotient: a x y x y a a Ex. ( ) = Concept 1: Simplifying Exponents LAWS of EXPONENTS: Test Question A. thru H. #1. = 1A. = 12 x #2. = 2B. 5 x #3. ( ) y = 3 3C. x 4 #4. ( ) = 4D. ( ) = #5. ( ) = 5E. ( ) = 3
Zero exponents: Zero and Negative Exponents x x n n n x n n 1 and x x n x 0, so x 0 = 1 LAWS of EXPONENTS: Test Questions 0 #6. ; x 0 x 6F. = ( ) = = Negative Exponents: x - n 1 = n x and ( ) = ( ) 4 a b ab 3 Ex. 1) Write 2 with only positive exponents. 2) Write with only positive exponents. 3) Write the following with only positive exponents: a) 3 2 ( y ) b) 2 5 y x 4) Simplify each. 4 3 6x y a) 7 5 3x y b) 4
Challenge Problem: Simplify. Use only positive exponents. Summary/Closure: Exit Ticket 5
SWBAT: Simplify rational exponents. Warm - Up: Day 2: Rational Exponents Rational Exponents Exponential Form Radical Form = ( ) power root Think : x = root power x or Concept 1: Rewrite each in exponential form. Teacher Modeled Student Try It! ( ) ( ) 6
Teacher Modeled Student Try It! ( ) ( ) ( ) ( ) Concept 2: Rewrite each in radical form. Teacher Modeled Student Try It! 7
Use exponents to write the radical expression. Let the variable represent positive numbers. Teacher Modeled Student Try It! Write the given expression, using a radical sign. Let the variables represent positive numbers Teacher Modeled Student Try It! ( ) 8
Practice: 3 2 1. If f(x) = x, find f(16). 2. Evaluate 3. 9
Challenge Summary/Closure Exit Ticket: 10
Day 3 - Exponential Functions SWBAT: Simplify rational exponents. Warm - Up: 11
An exponential function is of the form y = b 0, b 1, and x is a real number. Domain = {x x Real numbers} Range = {y y } Example 2: Graph y = ( ), y = on the graph below. Observations from above: (1) (2) (3) 12
Shifting the basic Exponential Graph f(x) = Transformation up down left right Reflect over x-axis Reflect over y-axis Transformation In examples 1 6, write an equation for each translation of y = 1. 2 units up 2. 1 units down 3. right 4 units 4. left 3 units 5. 1 units up, 4 units left 6. 3 units down, 5 units right 7. f(x) = means 8. f(x) = ( ) means 9. Graph f(x) = 10. Graph f(x) = 13
Example 11 14
Challenge SUMMARY Exit Ticket 15
Day 4 - Exponential Equations SWBAT: solve equations involving exponents. 2 Warm-Up: 1) What is the multiplicative inverse of? 3 2) What is the multiplicative inverse of? 1 3 1 1 a a a x a 1 x x x To solve an equation involving exponents: Ex. 1. Write the equation with only the variable term 1. on one side of the equation. 2. Divide both sides of the equation by the coefficient 2. of the variable term. 3. Raise both sides of the equation to the power that is 3. the reciprocal of the exponent of the variable. 4. Simplify the right side of the equation. 4. 5. Check the solution. 16
Concept - Solve for x in each exponential equation: Teacher Modeled Student Try It! 17
Challenge Summary/Closure Exit Ticket: 18
Day 5 - Exponential Equations involving like/unlike bases SWBAT: Solve Exponential Equations with like and unlike bases Warm-Up: 1) Express 36 as a power. 2) Express 81 as a power. 3) Express 32 as a power. Concept 1: Solving Exponential Equations with the like Bases If the bases are equal, the exponents must be equal. Ex. Solve for x: 3 x = 3 2x-2 To solve an equation with like bases: Ex. 1. Write the equation. 1. 2. Since the bases are alike, equate the exponents. 2. 3. Solve the resulting equation. 3. 19
Concept 1 - Solving Exponential Equations with the like Bases Teacher Modeled Student Try It! ( ) ( ) Concept 2: Solving Exponential Equations with Different Bases If possible, write each term as a power of the same base. Solve for x and check: 2 2x = 8 To solve an equation with unlike bases: Ex. 1. Write the equation. 1. 2. Change the higher base to a power of the smaller base. 2. 3. Simplify the higher base. 3. 4. Since the bases are alike, equate the exponents. 5. 5. Solve the resulting equation. 5. 20
Concept 2 - Solving Exponential Equations with the unlike Bases Teacher Modeled Student Try It! Concept 3: Solving Exponential Equations with Different Bases (neither base is the power of the other) If possible, write each term as a power of the same base. Solve for x and check: 9 x+1 = 27 x To solve an equation with unlike bases: Ex. 1. Write the equation. 1. 2. Change each base to a power of the same number. 2. 3. Simplify each base. 3. 4. Since the bases are alike, equate the exponents. 5. 5. Solve the resulting equation. 5. 21
Concept 3 - Solving Exponential Equations with the unlike Bases(neither base is the power of the other) Teacher Modeled Student Try It! 5 x-1 = (0.04) 2x ( ) 22
Challenge Summary/Closure Exit Ticket 23
Day 6 Review of Exponential Functions 24
c. d. 25
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48. Explain each transformation below from y =. a) y = b) y = c) y = d) y = e) y = f) y = ( ) 27
HW ANSWERS 28
Day 6 - REVIEW c. d. y = ( ) 48a. shift 2 right 48b. shift 2 down 48c. shift 4 right, up 7 48d. shift 1 left, down 8 48e. reflect over x-axis, up 1 48f. reflect y = 3 -x over y-axis, shift 6 right 29