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h(x) = (1.1)* X h(x) = (1.1)* -5 -1 5 10 y

h(x) = (1.1)* X h(x) = (1.1)* -5 -1 5 10 y

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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The image presents a table used to calculate \( h(x) = (1.1)^x \) for different values of \( x \). The table consists of two columns: 1. **Column 1 (x):** This column lists the x-values for which the function \( h(x) = (1.1)^x \) will be evaluated. The x-values in the table are: - \( x = -5 \) - \( x = -1 \) - \( x = 0 \) - \( x = 5 \) - \( x = 10 \) 2. **Column 2 \( (h(x) = (1.1)^x) \):** This column is intended for the computed results of the function \( h(x) = (1.1)^x \) corresponding to each x-value in the first column. However, the values are currently represented by empty boxes, indicating that calculations need to be performed and the results recorded. The table helps in understanding how exponential functions behave by plugging in different integer values of \( x \) into the exponential function \( h(x) = (1.1)^x \).
Transcribed Image Text:The image presents a table used to calculate \( h(x) = (1.1)^x \) for different values of \( x \). The table consists of two columns: 1. **Column 1 (x):** This column lists the x-values for which the function \( h(x) = (1.1)^x \) will be evaluated. The x-values in the table are: - \( x = -5 \) - \( x = -1 \) - \( x = 0 \) - \( x = 5 \) - \( x = 10 \) 2. **Column 2 \( (h(x) = (1.1)^x) \):** This column is intended for the computed results of the function \( h(x) = (1.1)^x \) corresponding to each x-value in the first column. However, the values are currently represented by empty boxes, indicating that calculations need to be performed and the results recorded. The table helps in understanding how exponential functions behave by plugging in different integer values of \( x \) into the exponential function \( h(x) = (1.1)^x \).
**Exponential Function Identification** **Problem Statement:** Find the exponential function \( f(x) = a^x \) whose graph is given. **Solution:** \( f(x) = \) **Graph Details:** - The graph presented is a curve that decreases from left to right, indicating a decay function. - The graph crosses the y-axis at \( y = 1 \), which suggests that \( a^0 = 1 \) (common for exponential functions). - A specific point on the graph is marked at \( (2, \frac{1}{4}) \). **Explanation:** The graph represents an exponential decay function. The point \( (2, \frac{1}{4}) \) indicates that when \( x = 2 \), the function \( f(x) = \frac{1}{4} \). We can use this point to solve for \( a \): \[ a^2 = \frac{1}{4} \] \[ a = \frac{1}{2} \] Thus, the exponential function is \( f(x) = \left(\frac{1}{2}\right)^x \).
Transcribed Image Text:**Exponential Function Identification** **Problem Statement:** Find the exponential function \( f(x) = a^x \) whose graph is given. **Solution:** \( f(x) = \) **Graph Details:** - The graph presented is a curve that decreases from left to right, indicating a decay function. - The graph crosses the y-axis at \( y = 1 \), which suggests that \( a^0 = 1 \) (common for exponential functions). - A specific point on the graph is marked at \( (2, \frac{1}{4}) \). **Explanation:** The graph represents an exponential decay function. The point \( (2, \frac{1}{4}) \) indicates that when \( x = 2 \), the function \( f(x) = \frac{1}{4} \). We can use this point to solve for \( a \): \[ a^2 = \frac{1}{4} \] \[ a = \frac{1}{2} \] Thus, the exponential function is \( f(x) = \left(\frac{1}{2}\right)^x \).
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