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3A: Analyze Exponential and Logarith Analyze following function and graph it. f(x) = 3(-1) + 1 :(00,00) (1,000) Domain: Range: Asymptote: HA 9=34x XHA n_y=3x Original Function: f(x) = logs(x-1)-2 Describe Transformation: Domain: Range: End Behavior. Os Right (1) f(x) = (and as left Asymptote: End Behavior: xy Newpt 10 TO Original Function: 5 25 2 myz logo 52 Describe Transformation:

3A: Analyze Exponential and Logarith Analyze following function and graph it. f(x) = 3(-1) + 1 :(00,00) (1,000) Domain: Range: Asymptote: HA 9=34x XHA n_y=3x Original Function: f(x) = logs(x-1)-2 Describe Transformation: Domain: Range: End Behavior. Os Right (1) f(x) = (and as left Asymptote: End Behavior: xy Newpt 10 TO Original Function: 5 25 2 myz logo 52 Describe Transformation:

Question
**Unit 3: Exponential and Logarithmic Functions** **3A: Analyze Exponential and Logarithmic Functions** ### Graph Analysis of Exponential and Logarithmic Functions #### Function 1: \( f(x) = 3 \cdot 4^{x-1} + 1 \) - **Graph Description:** - The graph shows an exponential curve. - Key values (x, y): - (0, 2) - (1, 5) - **Details:** - **Domain:** \( (-\infty, \infty) \) - **Range:** \( (1, \infty) \) - **Asymptote:** Horizontal asymptote at \( y = 1 \) - **End Behavior:** - As \( x \to \infty \), \( f(x) \to \infty \) - As \( x \to -\infty \), \( f(x) \to 1 \) - **Original Function:** \( y = 3 \times 4^x \) #### Function 2: \( f(x) = \log_5(x-1) - 2 \) - **Graph Description:** - The graph displays a logarithmic curve. - Key values (x, y): - (2, -3) - (11, 0) - **Details:** - **Domain:** \( (1, \infty) \) - **Range:** \( (-\infty, \infty) \) - **Asymptote:** Vertical asymptote at \( x = 1 \) - **End Behavior:** - As \( x \to 1^+\), \( f(x) \to -\infty \) - As \( x \to \infty \), \( f(x) \to \infty \) - **Original Function:** \( y = \log_5 x \) Both graphs require the identification of domain, range, asymptotes, and end behavior, facilitating a deeper understanding of these functions' characteristics. (Note: Descriptions of transformations in the graphs are not provided in the text.)
Transcribed Image Text:**Unit 3: Exponential and Logarithmic Functions** **3A: Analyze Exponential and Logarithmic Functions** ### Graph Analysis of Exponential and Logarithmic Functions #### Function 1: \( f(x) = 3 \cdot 4^{x-1} + 1 \) - **Graph Description:** - The graph shows an exponential curve. - Key values (x, y): - (0, 2) - (1, 5) - **Details:** - **Domain:** \( (-\infty, \infty) \) - **Range:** \( (1, \infty) \) - **Asymptote:** Horizontal asymptote at \( y = 1 \) - **End Behavior:** - As \( x \to \infty \), \( f(x) \to \infty \) - As \( x \to -\infty \), \( f(x) \to 1 \) - **Original Function:** \( y = 3 \times 4^x \) #### Function 2: \( f(x) = \log_5(x-1) - 2 \) - **Graph Description:** - The graph displays a logarithmic curve. - Key values (x, y): - (2, -3) - (11, 0) - **Details:** - **Domain:** \( (1, \infty) \) - **Range:** \( (-\infty, \infty) \) - **Asymptote:** Vertical asymptote at \( x = 1 \) - **End Behavior:** - As \( x \to 1^+\), \( f(x) \to -\infty \) - As \( x \to \infty \), \( f(x) \to \infty \) - **Original Function:** \( y = \log_5 x \) Both graphs require the identification of domain, range, asymptotes, and end behavior, facilitating a deeper understanding of these functions' characteristics. (Note: Descriptions of transformations in the graphs are not provided in the text.)
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