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What are the features of the function f(x) = 2 (3) - 2 graphed below? 12 -12-11-10-9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 11 12 The function f(x) is function with a The range of the function is , and it is The end behavior on the LEFT side is as the end behavior on the RIGHT side is as 20988EN 11 10 5 TO W AS 4 13 2 ܐ ܣ ܣ ܟ ܬ ܬ ܐ ܣ ܣ -2 -3 -4 -9 -10 -11 -12 <> asymptote of <> on its domain of and

What are the features of the function f(x) = 2 (3) - 2 graphed below? 12 -12-11-10-9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 11 12 The function f(x) is function with a The range of the function is , and it is The end behavior on the LEFT side is as the end behavior on the RIGHT side is as 20988EN 11 10 5 TO W AS 4 13 2 ܐ ܣ ܣ ܟ ܬ ܬ ܐ ܣ ܣ -2 -3 -4 -9 -10 -11 -12 <> asymptote of <> on its domain of and

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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### Features of the Function \( f(x) = 2 \left( \frac{1}{3} \right)^x - 2 \) **Graph Description:** The image features a graph of the function \( f(x) = 2 \left( \frac{1}{3} \right)^x - 2 \) on a Cartesian plane. The x-axis ranges from -12 to 12, and the y-axis ranges from -12 to 12. - **X-axis:** Originates at the center and extends from -12 to 12. - **Y-axis:** Originates at the center and extends from -12 to 12. - The graph of the function starts from the far left, growing towards the asymptote. - As \( x \) increases, the function value decreases rapidly and approaches \( y = -2 \) but never touches it. **Equation Analysis:** - **Exponential Decay:** The base \( \left( \frac{1}{3} \right) \) is less than 1, indicating that the function is an exponential decay. - **Horizontal Asymptote:** The graph has a horizontal asymptote at \( y = -2 \). **Feature Identification:** The function \( f(x) \) is an **exponential** function with a **horizontal** asymptote of \( -2 \). The function's range is \( (-2, \infty) \), and it is **decreasing** on its domain of \( (-\infty, \infty) \). - **End Behavior on the LEFT side:** As \( x \rightarrow -\infty \), \( f(x) \rightarrow \infty \). - **End Behavior on the RIGHT side:** As \( x \rightarrow \infty \), \( f(x) \rightarrow -2 \). This information helps understand how exponential decay functions behave and how to analyze their graph for significant features such as asymptotes and end behaviors.
Transcribed Image Text:### Features of the Function \( f(x) = 2 \left( \frac{1}{3} \right)^x - 2 \) **Graph Description:** The image features a graph of the function \( f(x) = 2 \left( \frac{1}{3} \right)^x - 2 \) on a Cartesian plane. The x-axis ranges from -12 to 12, and the y-axis ranges from -12 to 12. - **X-axis:** Originates at the center and extends from -12 to 12. - **Y-axis:** Originates at the center and extends from -12 to 12. - The graph of the function starts from the far left, growing towards the asymptote. - As \( x \) increases, the function value decreases rapidly and approaches \( y = -2 \) but never touches it. **Equation Analysis:** - **Exponential Decay:** The base \( \left( \frac{1}{3} \right) \) is less than 1, indicating that the function is an exponential decay. - **Horizontal Asymptote:** The graph has a horizontal asymptote at \( y = -2 \). **Feature Identification:** The function \( f(x) \) is an **exponential** function with a **horizontal** asymptote of \( -2 \). The function's range is \( (-2, \infty) \), and it is **decreasing** on its domain of \( (-\infty, \infty) \). - **End Behavior on the LEFT side:** As \( x \rightarrow -\infty \), \( f(x) \rightarrow \infty \). - **End Behavior on the RIGHT side:** As \( x \rightarrow \infty \), \( f(x) \rightarrow -2 \). This information helps understand how exponential decay functions behave and how to analyze their graph for significant features such as asymptotes and end behaviors.
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