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Use the graph of f to evaluate the following: 6 + f(x) 5 X 4 رها 3 N 1 1 2 4 5 The average rate of change of f from x = 0 to x = 2 =

Use the graph of f to evaluate the following: 6 + f(x) 5 X 4 رها 3 N 1 1 2 4 5 The average rate of change of f from x = 0 to x = 2 =

Intermediate Algebra
Intermediate Algebra
10th Edition
ISBN:9781285195728
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter9: Functions
Section9.CR: Review Problem Set
Problem 24CR: An outpatient operating room charges each patient a fixed amount per surgery plus an amount per...
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### Using the Graph of f to Evaluate the Following #### Graph Description The provided graph depicts a function \( f(x) \) plotted on a Cartesian coordinate system, where the x-axis ranges from 0 to 6 and the y-axis ranges from -1 to 6. The graph displays various linear segments connecting the following points: - \( (0, 3) \) - \( (1, 4) \) - \( (2, 1) \) - \( (3, 5) \) - \( (4, 0) \) - \( (5, 2) \) These points create a piecewise linear function with changes in direction at each specified point. #### Task Evaluate the average rate of change of \( f \) from \( x = 0 \) to \( x = 2 \). #### Calculation The average rate of change of a function \( f \) between two points \( x_1 \) and \( x_2 \) is given by the formula: \[ \text{Average Rate of Change} = \frac{f(x_2) - f(x_1)}{x_2 - x_1} \] For the interval \( [0, 2] \): - \( f(0) = 3 \) - \( f(2) = 1 \) Substitute these values into the formula: \[ \text{Average Rate of Change} = \frac{1 - 3}{2 - 0} = \frac{-2}{2} = -1 \] Therefore, the average rate of change of \( f \) from \( x = 0 \) to \( x = 2 \) is -1. Please input your answer in the provided box: \[ \text{The average rate of change of } f \text{ from } x = 0 \text{ to } x = 2 \text{ is } \boxed{-1} \]
Transcribed Image Text:### Using the Graph of f to Evaluate the Following #### Graph Description The provided graph depicts a function \( f(x) \) plotted on a Cartesian coordinate system, where the x-axis ranges from 0 to 6 and the y-axis ranges from -1 to 6. The graph displays various linear segments connecting the following points: - \( (0, 3) \) - \( (1, 4) \) - \( (2, 1) \) - \( (3, 5) \) - \( (4, 0) \) - \( (5, 2) \) These points create a piecewise linear function with changes in direction at each specified point. #### Task Evaluate the average rate of change of \( f \) from \( x = 0 \) to \( x = 2 \). #### Calculation The average rate of change of a function \( f \) between two points \( x_1 \) and \( x_2 \) is given by the formula: \[ \text{Average Rate of Change} = \frac{f(x_2) - f(x_1)}{x_2 - x_1} \] For the interval \( [0, 2] \): - \( f(0) = 3 \) - \( f(2) = 1 \) Substitute these values into the formula: \[ \text{Average Rate of Change} = \frac{1 - 3}{2 - 0} = \frac{-2}{2} = -1 \] Therefore, the average rate of change of \( f \) from \( x = 0 \) to \( x = 2 \) is -1. Please input your answer in the provided box: \[ \text{The average rate of change of } f \text{ from } x = 0 \text{ to } x = 2 \text{ is } \boxed{-1} \]
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