Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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**Title: Matching Exponential Functions** **Task:** Match the graph to the correct exponential functions. Select all that apply. **Graph Description:** - The graph is a plotted curve on a coordinate grid. - It shows an exponential decay, approaching zero but remaining above the x-axis as x increases. - As x decreases, the graph curves downwards steeply towards negative infinity on the y-axis. **Coordinate Details:** - The graph crosses the y-axis at or above 2. - The curve steeply declines towards the right, indicating a negative exponent effect. **Function Options:** 1. \( y = -2(3)^x \) 2. \( y = 2(3)^{-x} \) 3. \( y = 2\left(\frac{1}{3}\right)^x \) 4. \( y = 2(3)^x \) 5. \( y = 2\left(\frac{1}{3}\right)^{-x} \) **Identify the Correct Function(s):** - Observing the direction and behavior of the exponential decay, the probable matching function is: - \( y = 2(3)^{-x} \) (Selected) This function accurately reflects the graph’s exponential decay features, where the base of the exponent is inverse and results in the described descending slope of the graph.
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Transcribed Image Text:**Title: Matching Exponential Functions** **Task:** Match the graph to the correct exponential functions. Select all that apply. **Graph Description:** - The graph is a plotted curve on a coordinate grid. - It shows an exponential decay, approaching zero but remaining above the x-axis as x increases. - As x decreases, the graph curves downwards steeply towards negative infinity on the y-axis. **Coordinate Details:** - The graph crosses the y-axis at or above 2. - The curve steeply declines towards the right, indicating a negative exponent effect. **Function Options:** 1. \( y = -2(3)^x \) 2. \( y = 2(3)^{-x} \) 3. \( y = 2\left(\frac{1}{3}\right)^x \) 4. \( y = 2(3)^x \) 5. \( y = 2\left(\frac{1}{3}\right)^{-x} \) **Identify the Correct Function(s):** - Observing the direction and behavior of the exponential decay, the probable matching function is: - \( y = 2(3)^{-x} \) (Selected) This function accurately reflects the graph’s exponential decay features, where the base of the exponent is inverse and results in the described descending slope of the graph.
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