CL-Math Average Rate of Change, Piece-wise defined functions How does the slope of the line for each question (a)-(d) changes as you are closing the gap? What prediction can you make about slope of a line passing through two points and average rate of change of a function on an interval defined by the same two points? A table is provided below to summarize your observation. f(x) = 2x² +2: Interval [a, b] On [0, 2] On [0, 1] On [0,.5] Worksheet 6 On [0, x] f(b) f(a) Average Rate of Change f(b) - f(a) b-a (-21212+2)-1-2101²+20 (2)-10)=4 (2141421-1211122) (1)-10) Slope of the line = 2 (21.5)2+2)-(2/0)2+2) 1.57-101 =1 (26x12 +21-12101272) (x)-10) = 2X function f(x) = x. Now can you rewrite the function f(x)
CL-Math Average Rate of Change, Piece-wise defined functions How does the slope of the line for each question (a)-(d) changes as you are closing the gap? What prediction can you make about slope of a line passing through two points and average rate of change of a function on an interval defined by the same two points? A table is provided below to summarize your observation. f(x) = 2x² +2: Interval [a, b] On [0, 2] On [0, 1] On [0,.5] Worksheet 6 On [0, x] f(b) f(a) Average Rate of Change f(b) - f(a) b-a (-21212+2)-1-2101²+20 (2)-10)=4 (2141421-1211122) (1)-10) Slope of the line = 2 (21.5)2+2)-(2/0)2+2) 1.57-101 =1 (26x12 +21-12101272) (x)-10) = 2X function f(x) = x. Now can you rewrite the function f(x)
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![**CL-Math Worksheet 6: Average Rate of Change, Piece-wise Defined Functions**
How does the slope of the line for each question (a)–(d) change as you are closing the gap? What prediction can you make about the slope of a line passing through two points and the average rate of change of a function on an interval defined by the same two points? A table is provided below to summarize your observation.
Given Function:
\( f(x) = 2x^2 + 2 \)
| Interval [a, b] | f(b) | f(a) | Average Rate of Change \(\frac{f(b) - f(a)}{b - a}\) | Slope of the line |
|-----------------|-------------------|-------------------|-----------------------------------------------------|-------------------|
| On [0, 2] | \(-2(2)^2 + 2\) | \(-2(0)^2 + 2\) | \(\frac{-1 - 2}{2 - 0} = -\frac{3}{2}\)* | 4 |
| On [0, 1] | \(2(1)^2 + 2\) | \(2(0)^2 + 2\) | \(\frac{2 - 2}{1 - 0} = 2\) | 2 |
| On [0, 0.5] | \(2(0.5)^2 + 2\) | \(2(0)^2 + 2\) | \(\frac{0.5 - 2}{0.5 - 0} = 1\) | 1 |
| On [0, x] | \(2(x)^2 + 2\) | \(2(0)^2 + 2\) | \(\frac{2x^2 + 2 - 2}{x - 0} = 2x\) | 2x |
**Note**: *There seems to be an inconsistency in the transcription of the average rate of change on [0, 2]. The correct computation should be double-checked for accuracy.
The worksheet explores how the average rate of change of a function \( f(x) = 2x^2 + 2 \) varies](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbef6184d-e4ed-4e37-a8bf-e63dcfbc4d4c%2Fb706deda-c4db-441c-984f-5676aab58c2d%2F0ctwj7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**CL-Math Worksheet 6: Average Rate of Change, Piece-wise Defined Functions**
How does the slope of the line for each question (a)–(d) change as you are closing the gap? What prediction can you make about the slope of a line passing through two points and the average rate of change of a function on an interval defined by the same two points? A table is provided below to summarize your observation.
Given Function:
\( f(x) = 2x^2 + 2 \)
| Interval [a, b] | f(b) | f(a) | Average Rate of Change \(\frac{f(b) - f(a)}{b - a}\) | Slope of the line |
|-----------------|-------------------|-------------------|-----------------------------------------------------|-------------------|
| On [0, 2] | \(-2(2)^2 + 2\) | \(-2(0)^2 + 2\) | \(\frac{-1 - 2}{2 - 0} = -\frac{3}{2}\)* | 4 |
| On [0, 1] | \(2(1)^2 + 2\) | \(2(0)^2 + 2\) | \(\frac{2 - 2}{1 - 0} = 2\) | 2 |
| On [0, 0.5] | \(2(0.5)^2 + 2\) | \(2(0)^2 + 2\) | \(\frac{0.5 - 2}{0.5 - 0} = 1\) | 1 |
| On [0, x] | \(2(x)^2 + 2\) | \(2(0)^2 + 2\) | \(\frac{2x^2 + 2 - 2}{x - 0} = 2x\) | 2x |
**Note**: *There seems to be an inconsistency in the transcription of the average rate of change on [0, 2]. The correct computation should be double-checked for accuracy.
The worksheet explores how the average rate of change of a function \( f(x) = 2x^2 + 2 \) varies
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