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Name ________________________________________ Date __________________ Class __________________ LESSON 12-2 Geometric Sequences Practice and Problem Solving: A/B Each rule represents a geometric sequence. If the given rule is recursive, write it as an explicit rule. If the rule is explicit, write it as a recursive rule. Assume that f(1) is the first term of the sequence. 1. f(n) = 11(2)n−1 2. f(1) = 2.5; f(n) = f(n − 1) i 3.5 for n ≥ 2 ________________________________________ 3. f(1) = 27; f(n) = f(n − 1) i ________________________________________ 1 for n ≥ 2 3 4. f(n) = −4(0.5)n−1 ________________________________________ ________________________________________ Write an explicit rule for each geometric sequence based on the given terms from the sequence. Assume that the common ratio r is positive. 5. a1 = 90 and a2 = 360 6. a1 = 16 and a3 = 4 ________________________________________ ________________________________________ 7. a1 = 2 and a5 = 162 8. a2 = 30 and a3 = 10 ________________________________________ ________________________________________ 9. a4 = 135 and a5 = 405 10. a3 = 400 and a5 = 256 ________________________________________ ________________________________________ 11. a2 = 80 and a5 = 10 12. a4 = 22 and a7 = 0.022 ________________________________________ ________________________________________ A bank account earns a constant rate of interest each month. The account was opened on March 1 with $18,000 in it. On April 1, the balance in the account was $18,045. Use this information for Problems 13–15. 13. Write an explicit rule and a recursive rule that can be used to find A(n), the balance after n months. _________________________________________________________________________________________ 14. Find the balance after 5 months. _________________________________________________________________________________________ 15. Find the balance after 5 years. _________________________________________________________________________________________ Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor. 187 Graphing Exponential Functions Name Period # x Ex 1: The function y = 3 is called an _____________________________ function because the exponent is a ____________________________. Now, let’s look at how to graph the exponential function x -3 y = 3x 1 1 y = 3( −3) = 3 = 27 3 y y = 3x . (x, y) -2 -1 0 1 2 3 Definition 1: Since the y values increase as the x values increase in the example above, this is what we call exponential ___________________________. (The graph goes up the hill from left to right) QUESTION: In the exponential function y = 3 x , the y-values can never equal or be less than ____________. Definition 2: Since the y-value can NEVER equal zero in this function, there is a horizontal __________________________ at y = 0. Ex 2: By looking at the graph above, list the domain and range of the function DOMAIN: RANGE: y = 3x x ⎛1⎞ Ex 3: Now, let’s look at how to graph the exponential function y = ⎜ ⎟ . ⎝3⎠ ⎛1⎞ y =⎜ ⎟ ⎝3⎠ x x y (x, y) -3 -2 -1 0 1 2 3 Definition 3: Since the y values decrease as the x values increase in the example above, this is what we call exponential ___________________________. (The graph goes down the hill from left to right) QUESTION: Is there an asymptote? If so, where is it? ⎛1⎞ Ex 4: By looking at the graph above, list the domain and range of the function y = ⎜ ⎟ ⎝3⎠ x DOMAIN: RANGE: Tell whether the functions below show exponential GROWTH or DECAY. ⎛1⎞ 5) y = ⎜ ⎟ ⎝4⎠ 8) y =5 x x 6) y = 2x 9) x y=0 7) y =1x ⎛2⎞ 10) y = ⎜ ⎟ ⎝3⎠ x Graphing Exponential Functions Practice Worksheet Name Period # Graph the following functions and tell whether they show exponential growth or decay. 1) x y = 2x y (x, y) -3 -2 -1 0 1 2 3 Does the function above show exponential GROWTH or DECAY? 2) x ⎛1⎞ y =⎜ ⎟ ⎝2⎠ x y (x, y) -3 -2 -1 0 1 2 3 Does the function above show exponential GROWTH or DECAY? 3) y = 1x x y (x, y) -3 -2 -1 0 1 2 3 Does the function above show exponential GROWTH or DECAY? Tell whether the functions below show exponential GROWTH or DECAY. 4) y=9 x ⎛2⎞ 7) y = ⎜ ⎟ ⎝7⎠ x ⎛1⎞ 5) y = ⎜ ⎟ ⎝5⎠ x ⎛5⎞ 8) y = ⎜ ⎟ ⎝6⎠ x 6) y = 4x 9) y = 0x Algebra 1 Unit: Exponential Functions Homework Name Date Hour Graphing Exponential Functions Worksheet #2 Directions: Answer all questions. Show all work!!! Sketch the graph of each function. Then, state the Domain, Range, and Y-intercept, and change of Y-values of the function. 1. y = 8 • ( 12 ) x X Y -1 0 1 2 3 4 5 6 Domain: Range: Y-Intercept: ( , ) Change in Y-Values: Growth or Decay? ____________ 1 7 2 2. y = • 2x X Y -4 -3 -2 -1 0 1 2 3 4 Domain: Range: Y-Intercept: ( , ) Change in Y-Values: Growth or Decay? ____________ 2 x 3. y =− 6 • ( 12 ) X Y -2 -1 0 1 2 3 4 5 6 7 Domain: Range: Y-Intercept: ( , ) Change in Y-Values: Growth or Decay? ____________ 3 4. y = 0.5 x X Y -3 -2 -1 0 1 2 3 Domain: Range: Y-Intercept: ( , ) Change in Y-Values (b) : Growth or Decay? ____________ 4 Kuta Software - Infinite Algebra 1 Name___________________________________ Exponential Functions Date________________ Period____ Evaluate each function at the given value. 1) f ( x) = x at x 2) f (n) = n at n 3) f (n) = n at n 4) g( x) = x 6) f ( x) x () at x Sketch the graph of each function. 5) f ( x) x () y y x ©C 0290x1P2E lKkuttZaD KSaocfKtZwIaErge4 QL6L8CF.o N OAYl4lE Cr2ivgehetKs5 Jr6e1sreMrSvOeRdo.D O iMYawdvev ywyi2tuhM LI6n1fgiAnriDtReH KAqltgFe9bMrSan Y11.n -1- x Worksheet by Kuta Software LLC 7) f ( x) x 8) f ( x) () x y x y x Write an equation for each graph. 9) 10) y x ©u t2o0s162N aKZu7tPai 8SBo0fetWwAa9rfei mL9LsCb.D q tAUlol8 4rwiXgKhTt4sm grceQsxesrdveePdo.7 S 4MmaVdwet PwRiXtmhW oI1nCfki3nniRtfe1 fAZlJg6eSbirdav Z1j.E -2- y x Worksheet by Kuta Software LLC
