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aphoryf jappears t Determine the key features of the function f(x) = 10+¹ +5. Identify the x-intercept, the y-intercept, any asymptotes, and the end behavior of the function.

aphoryf jappears t Determine the key features of the function f(x) = 10+¹ +5. Identify the x-intercept, the y-intercept, any asymptotes, and the end behavior of the function.

College Algebra
College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter3: Functions
Section3.2: Domain And Range
Problem 2SE: How do we determine the domain of a function defined by an equation?
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Question
#### Key Features of the Function Determine the key features of the function \( f(x) = 10^{x+1} - 5 \). Identify the x-intercept, the y-intercept, any asymptotes, and the end behavior of the function.
Transcribed Image Text:#### Key Features of the Function Determine the key features of the function \( f(x) = 10^{x+1} - 5 \). Identify the x-intercept, the y-intercept, any asymptotes, and the end behavior of the function.
The function \( g(x) \) is a transformation of the function \( f(x) = 3^x \). The coordinate plane shows the graph of both functions. ### Graph Explanation: - The graph includes two functions represented in different colors: - **Function \( f(x) = 3^x \):** This is shown in purple. - **Function \( g(x) \):** This is shown in teal. The exact transformation is not specified, but it appears to be a reflection over the y-axis or another form of transformation. ### Key Points on the Graph: - **Purple Graph (\( f(x) = 3^x \)):** - The function moves upward rapidly. - Key points include (0, 1), (1, 3), and (2, 9). - **Teal Graph (\( g(x) \)):** - The function appears to decrease as x increases, indicating a transformation such as reflection. - Key points include (0, 0), (2, -2), and it seems to cross the x-axis and descend further. ### Axes: - The horizontal axis is labeled as \( x \). - The vertical axis is labeled as \( y \). - Both axes range from -8 to 8 for \( x \), and -8 to 8 for \( y \). The grid lines on the graph help to clarify the position of the key points and the shape of each function.
Transcribed Image Text:The function \( g(x) \) is a transformation of the function \( f(x) = 3^x \). The coordinate plane shows the graph of both functions. ### Graph Explanation: - The graph includes two functions represented in different colors: - **Function \( f(x) = 3^x \):** This is shown in purple. - **Function \( g(x) \):** This is shown in teal. The exact transformation is not specified, but it appears to be a reflection over the y-axis or another form of transformation. ### Key Points on the Graph: - **Purple Graph (\( f(x) = 3^x \)):** - The function moves upward rapidly. - Key points include (0, 1), (1, 3), and (2, 9). - **Teal Graph (\( g(x) \)):** - The function appears to decrease as x increases, indicating a transformation such as reflection. - Key points include (0, 0), (2, -2), and it seems to cross the x-axis and descend further. ### Axes: - The horizontal axis is labeled as \( x \). - The vertical axis is labeled as \( y \). - Both axes range from -8 to 8 for \( x \), and -8 to 8 for \( y \). The grid lines on the graph help to clarify the position of the key points and the shape of each function.
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