Answered: The graph of y=f(x) to the right gives…

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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The graph of y=f(x) to the right gives the speed limit y along a rural highway x miles from its starting point.

(a) What are the maximum and minimum speed limits along this stretch of highway? Estimate the miles of highway with a speed limit of 50 miles per hour.

(b) Evaluate f(16), f(32), and f(36). And at what x-values is the graph discontinuous? Interpret each discontinuity.

a) Along this stretch of highway, the maximum speed limit is ___ miles per hour and the minimum speed limit is ____ miles per hour.

There are ___ miles of highway with a speed limit of 50 miles per hour.

b) Evaluate.
f(16) = _____
f(32) = _____
f(36) = _____

At what x-values is the graph discontinuous? _____ (Use a comma to seperate answers.)

Interpret the discontinuities. Choose the correct interpretaion below.

A) The speed limit changes at each discontinuity.
B) The road changes names at each discontinuity.
C) There is no speed limit data for the discontinuities.
D) The altitude changes at each discontinuity.

The image displays a line graph that depicts the speed limit (in mph) as a function of distance (in miles).

**Graph Details:**

- **X-Axis (Horizontal):** Represents the distance, ranging from 0 to 40 miles.
- **Y-Axis (Vertical):** Represents the speed limit, ranging from 0 to 60 mph.

**Data Points and Trends:**

1. From 0 to 16 miles, the speed limit is consistently 50 mph.
2. At 16 miles, the speed limit drops to 40 mph, remaining constant until 24 miles.
3. From 24 to 28 miles, the speed limit increases back to 50 mph.
4. At 32 miles, the speed limit decreases to 45 mph and stays constant through 36 miles.
5. Finally, at 40 miles, the speed limit returns to 50 mph.

This graph effectively illustrates changes in speed limits over a specific distance, which can be useful for understanding traffic regulations over a journey.

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