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9(x) f(a) -10-9-8-7-6-5-4-3-2 The graphs of f(x)-- Ox-Intercept O Vertical asymptote O Range O End behavior 10 9 8 7 6 5 4 4 5 6 7 8 9 10 -0 -10 2x and g(x) = -log(x + 3) + 1 have which of the following features in common? X+4 57779

9(x) f(a) -10-9-8-7-6-5-4-3-2 The graphs of f(x)-- Ox-Intercept O Vertical asymptote O Range O End behavior 10 9 8 7 6 5 4 4 5 6 7 8 9 10 -0 -10 2x and g(x) = -log(x + 3) + 1 have which of the following features in common? X+4 57779

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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**Graphs of Functions \( f(x) = \frac{2x}{x + 4} \) and \( g(x) = \log_3(x + 3) + 1 \)** The image contains a Cartesian coordinate system with two graphed functions, \( f(x) \) and \( g(x) \). The functions shown are: 1. \( f(x) = \frac{2x}{x + 4} \) 2. \( g(x) = \log_3(x + 3) + 1 \) ### Detailed Analysis of the Graphs - **Graph of \( f(x) = \frac{2x}{x + 4} \)** - This graph is represented in blue. - It appears to have a vertical asymptote near \( x = -4 \), where the function is undefined. - The graph crosses the x-axis (x-intercept) approximately at \( x = 0 \). - The horizontal asymptote seems to be \( y = 2 \), indicating the end behavior of the function as \( x \) increases or decreases without bound. - **Graph of \( g(x) = \log_3(x + 3) + 1 \)** - This graph is represented in orange. - It shows a vertical asymptote at \( x = -3 \), where the logarithmic function is undefined. - The graph increases rapidly as \( x \) moves away from \( -3 \). - The function does not intersect the x-axis within the visible range. ### Features to Compare The question posed to the viewer is to find which feature is common between the two functions. **Options:** 1. **x-Intercept** 2. **Vertical Asymptote** 3. **Range** 4. **End Behavior** ### Explanation of Each Option 1. **x-Intercept**: - The x-intercept is the point where the graph crosses the x-axis. \( f(x) \) seems to cross the x-axis, whereas \( g(x) \) does not. 2. **Vertical Asymptote**: - Both graphs have vertical asymptotes but at different x-values: \( f(x) \) has one at \( x = -4 \) and \( g(x) \) at \( x = -3 \). 3. **Range**:
Transcribed Image Text:**Graphs of Functions \( f(x) = \frac{2x}{x + 4} \) and \( g(x) = \log_3(x + 3) + 1 \)** The image contains a Cartesian coordinate system with two graphed functions, \( f(x) \) and \( g(x) \). The functions shown are: 1. \( f(x) = \frac{2x}{x + 4} \) 2. \( g(x) = \log_3(x + 3) + 1 \) ### Detailed Analysis of the Graphs - **Graph of \( f(x) = \frac{2x}{x + 4} \)** - This graph is represented in blue. - It appears to have a vertical asymptote near \( x = -4 \), where the function is undefined. - The graph crosses the x-axis (x-intercept) approximately at \( x = 0 \). - The horizontal asymptote seems to be \( y = 2 \), indicating the end behavior of the function as \( x \) increases or decreases without bound. - **Graph of \( g(x) = \log_3(x + 3) + 1 \)** - This graph is represented in orange. - It shows a vertical asymptote at \( x = -3 \), where the logarithmic function is undefined. - The graph increases rapidly as \( x \) moves away from \( -3 \). - The function does not intersect the x-axis within the visible range. ### Features to Compare The question posed to the viewer is to find which feature is common between the two functions. **Options:** 1. **x-Intercept** 2. **Vertical Asymptote** 3. **Range** 4. **End Behavior** ### Explanation of Each Option 1. **x-Intercept**: - The x-intercept is the point where the graph crosses the x-axis. \( f(x) \) seems to cross the x-axis, whereas \( g(x) \) does not. 2. **Vertical Asymptote**: - Both graphs have vertical asymptotes but at different x-values: \( f(x) \) has one at \( x = -4 \) and \( g(x) \) at \( x = -3 \). 3. **Range**:
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