For the graph below, calculate the following quantities. y=#(x) y=g{x} y/(5) if y(x) = f(r)g(x) a. b. y(2) if y(x) = g(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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**Problem 7**: For the graph below, calculate the following quantities.

The graph depicts two functions, \( y = f(x) \) and \( y = g(x) \). 

- The function \( y = f(x) \) is represented by a blue line. This line starts on the y-axis at \( y = -2 \) and increases, intersecting the points (0, -2), (2, 2), and (5, -4) through (6, -2).

- The function \( y = g(x) \) is represented by a red line. The line decreases from the point (0, 4) through (2, 1), and intersects (7, -3).

**Questions:**

a. \( y'(5) \) if \( y(x) = f(x)g(x) \)

b. \( y'(2) \) if \( y(x) = g(f(x)) \)
Transcribed Image Text:**Problem 7**: For the graph below, calculate the following quantities. The graph depicts two functions, \( y = f(x) \) and \( y = g(x) \). - The function \( y = f(x) \) is represented by a blue line. This line starts on the y-axis at \( y = -2 \) and increases, intersecting the points (0, -2), (2, 2), and (5, -4) through (6, -2). - The function \( y = g(x) \) is represented by a red line. The line decreases from the point (0, 4) through (2, 1), and intersects (7, -3). **Questions:** a. \( y'(5) \) if \( y(x) = f(x)g(x) \) b. \( y'(2) \) if \( y(x) = g(f(x)) \)
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