For the table below, identify both a linear function f(x) and an exponential function g(x) that fits the two given values. Complete the table and graph for each function. 1 3 4. Linear f(x) 10 Exponential g(x) a) Linear Function f(x) = Find the average rate of change of f(x) on the interval 0sxs1. %3D Find the average rate of change of f(x) on the interval 2sxs3. b) Exponential Function g(x) = Find the average rate of change of g(x) on the interval 0 sxs1. Find the average rate of change of g(x) on the interval 2 sxs3. c) What is the first integer value of x for which g(x) is less than 0.001?

Algebra and Trigonometry (6th Edition)
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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For the table below, identify both a linear function f(x) and an exponential function g(x) that fits the two given values. Complete the table and graph for each function.

| x | 0 | 1 | 2 | 3 | 4 | x |
|---|---|---|---|---|---|---|
| Linear f(x) |   |   |   |   |   |   |
| Exponential g(x) |   | 10 | 5 |   |   |   |

### a) Linear Function
\[ f(x) = \]
Find the average rate of change of \( f(x) \) on the interval \( 0 \leq x \leq 1 \).

Find the average rate of change of \( f(x) \) on the interval \( 2 \leq x \leq 3 \).

### b) Exponential Function
\[ g(x) = \]
Find the average rate of change of \( g(x) \) on the interval \( 0 \leq x \leq 1 \).

Find the average rate of change of \( g(x) \) on the interval \( 2 \leq x \leq 3 \).

### c) What is the first integer value of x for which \( g(x) \) is less than 0.001?

### Explanation of Graph

The graph on the left side of the image is a two-dimensional coordinate grid. The x-axis is labeled with values from 0 to 4, and the y-axis is similarly labeled with values from 0 to 4. This grid is intended to plot the values of both the linear function \( f(x) \) and the exponential function \( g(x) \) based on the completed table values.

Ensure to plot the points for each function accurately once the missing values in the table are calculated. For the linear function, draw a straight line through the plotted points. For the exponential function, note that the points should form a curve that accurately reflects the rapid change characteristic of exponential growth or decay.

The table and graph need to be correctly completed based on the properties and forms of linear and exponential functions.
Transcribed Image Text:For the table below, identify both a linear function f(x) and an exponential function g(x) that fits the two given values. Complete the table and graph for each function. | x | 0 | 1 | 2 | 3 | 4 | x | |---|---|---|---|---|---|---| | Linear f(x) | | | | | | | | Exponential g(x) | | 10 | 5 | | | | ### a) Linear Function \[ f(x) = \] Find the average rate of change of \( f(x) \) on the interval \( 0 \leq x \leq 1 \). Find the average rate of change of \( f(x) \) on the interval \( 2 \leq x \leq 3 \). ### b) Exponential Function \[ g(x) = \] Find the average rate of change of \( g(x) \) on the interval \( 0 \leq x \leq 1 \). Find the average rate of change of \( g(x) \) on the interval \( 2 \leq x \leq 3 \). ### c) What is the first integer value of x for which \( g(x) \) is less than 0.001? ### Explanation of Graph The graph on the left side of the image is a two-dimensional coordinate grid. The x-axis is labeled with values from 0 to 4, and the y-axis is similarly labeled with values from 0 to 4. This grid is intended to plot the values of both the linear function \( f(x) \) and the exponential function \( g(x) \) based on the completed table values. Ensure to plot the points for each function accurately once the missing values in the table are calculated. For the linear function, draw a straight line through the plotted points. For the exponential function, note that the points should form a curve that accurately reflects the rapid change characteristic of exponential growth or decay. The table and graph need to be correctly completed based on the properties and forms of linear and exponential functions.
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