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Directions: Follow the instructions to go through the simulation. Respond to the questions and prompts in the orange boxes. ocabulary: asymptote, base, domain, exponent, exponential function, inverse function, logarithmic unction, range rior Knowledge Questions (Do these BEFORE using the Gizmo.) An exponent indicates repeated multiplication. A function with a variable in the exponent is called an exponential function. A. Evaluate the exponential expressions below. (Recall that negative exponents indicate fractions. 1 1 For example, 2= 2 = 8.) 2² = 9 2² = U 2¹= 2 2⁰= | 2-¹ = 2² = B. Based on your answers above, what points must lie on the graph of y = 2¹? (3,8), (2, 1), (1,2), (0,1),(-¹;²7²), (-2, ²²), (-3, 7). ²6. iqueras 2³ = 1 8

Directions: Follow the instructions to go through the simulation. Respond to the questions and prompts in the orange boxes. ocabulary: asymptote, base, domain, exponent, exponential function, inverse function, logarithmic unction, range rior Knowledge Questions (Do these BEFORE using the Gizmo.) An exponent indicates repeated multiplication. A function with a variable in the exponent is called an exponential function. A. Evaluate the exponential expressions below. (Recall that negative exponents indicate fractions. 1 1 For example, 2= 2 = 8.) 2² = 9 2² = U 2¹= 2 2⁰= | 2-¹ = 2² = B. Based on your answers above, what points must lie on the graph of y = 2¹? (3,8), (2, 1), (1,2), (0,1),(-¹;²7²), (-2, ²²), (-3, 7). ²6. iqueras 2³ = 1 8

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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el Gizmos Name: Student Exploration: Logarithmic Functions Directions: Follow the instructions to go through the simulation. Respond to the questions and prompts in the orange boxes. Vocabulary: asymptote, base, domain, exponent, exponential function, inverse function, logarithmic function, range Prior Knowledge Questions (Do these BEFORE using the Gizmo.) 1. An exponent indicates repeated multiplication. A function with a variable in the exponent is called an exponential function A. Evaluate the exponential expressions below. (Recall that negative exponents indicate fractions. For example, 2= 2 = 8.) 2³ = Date: 22 = 2¹ = 2 2⁰ = 2-1 = I 2-² = 2 = B. Based on your answers above, what points must lie on the graph of y = 2¹? [(3,8), (2,4), (1,2), (0,1),(-¹,²²), (-2, ²), (-3, 7)... 2. An inverse function reverses the x- and y-values of the original function. What points must lie on the inverse of y = 2*? (8,3), (4,2), (2,0/(110), (+,-1) i (+₁-2), (2, 3).... Gizmo Warm-up: The inverse of an exponential function with base b (y= b) is called a logarithmic function, also with base b (y = log(x)). So, the inverse of y= 2* is y = log₂ (x). If a point lies on the raph of y = 2* (say, (3, 8)), then a corresponding point, with x and y flipped, lies on y = log₂ (x) (say, (8, )). In the Logarithmic Functions Gizmo, you can explore related logarithmic and exponential nctions. in the CONTROLS tab, set b to 2 to graph y = log₂(x). (To quickly set the value of a slider, type e number into the text box to the right of the slider and press Enter.) Use the slider to vary the value of b. How does this affect the graph? as the value of b deceases the graph of Logx) and y=b² approaches y=x (line). Also, Log, x approchase X-axis X-intercept remains the Seme Vary b again. What happens to the x-intercept? Reproduction for educational use only. Public sharing or posting prohibited. Ⓒ2020 ExploreLearning TM All rights reserved
Transcribed Image Text:el Gizmos Name: Student Exploration: Logarithmic Functions Directions: Follow the instructions to go through the simulation. Respond to the questions and prompts in the orange boxes. Vocabulary: asymptote, base, domain, exponent, exponential function, inverse function, logarithmic function, range Prior Knowledge Questions (Do these BEFORE using the Gizmo.) 1. An exponent indicates repeated multiplication. A function with a variable in the exponent is called an exponential function A. Evaluate the exponential expressions below. (Recall that negative exponents indicate fractions. For example, 2= 2 = 8.) 2³ = Date: 22 = 2¹ = 2 2⁰ = 2-1 = I 2-² = 2 = B. Based on your answers above, what points must lie on the graph of y = 2¹? [(3,8), (2,4), (1,2), (0,1),(-¹,²²), (-2, ²), (-3, 7)... 2. An inverse function reverses the x- and y-values of the original function. What points must lie on the inverse of y = 2*? (8,3), (4,2), (2,0/(110), (+,-1) i (+₁-2), (2, 3).... Gizmo Warm-up: The inverse of an exponential function with base b (y= b) is called a logarithmic function, also with base b (y = log(x)). So, the inverse of y= 2* is y = log₂ (x). If a point lies on the raph of y = 2* (say, (3, 8)), then a corresponding point, with x and y flipped, lies on y = log₂ (x) (say, (8, )). In the Logarithmic Functions Gizmo, you can explore related logarithmic and exponential nctions. in the CONTROLS tab, set b to 2 to graph y = log₂(x). (To quickly set the value of a slider, type e number into the text box to the right of the slider and press Enter.) Use the slider to vary the value of b. How does this affect the graph? as the value of b deceases the graph of Logx) and y=b² approaches y=x (line). Also, Log, x approchase X-axis X-intercept remains the Seme Vary b again. What happens to the x-intercept? Reproduction for educational use only. Public sharing or posting prohibited. Ⓒ2020 ExploreLearning TM All rights reserved
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