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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Transcribed Image Text:### Educational Assessment: Absolute Value Inequalities
This section explores the concept of absolute value inequalities, focusing on finding the range of values that satisfy given conditions regarding distances from a specified point.
#### a. Distance from 7 Less Than 8
Identify all values of \( x \) such that the distance from 7 is less than 8. Select all statements that correctly represent this condition:
- \(\lvert x - 7 \rvert \leq 8\)
- \(\lvert x - 8 \rvert < 7\) **(Selected)**
- \(\lvert x - 7 \rvert < 8\)
- \(\lvert x - 8 \rvert > 7\)
#### b. Distance from 3 More Than 0.8
Determine all values of \( r \) such that their distance from 3 is more than 0.8. Choose all applicable options:
- \(\lvert r - 3 \rvert > 0.8\)
- \(\lvert r - 0.8 \rvert > 3\)
- \(\lvert r - 3 \rvert < 0.8\)
- \(\lvert r - 0.8 \rvert < 0.8\)
#### c. Distance from -5 No More Than 3.5
Identify all possible values of \( s \) with a distance from -5 no more than 3.5. Select all valid conditions:
- \(\lvert s + 5 \rvert < 3.5\) **(Selected)**
- \(\lvert s + 5 \rvert \leq 3.5\)
- \(\lvert s - 5 \rvert < 3.5\)
- \(\lvert s - 5 \rvert \leq 3.5\)
**Note:** Each question has boxes labeled Box 1, Box 2, and Box 3, inviting the selection of all correct answers.
This exercise aids in understanding how absolute values can represent distances on a number line and solving inequalities involving these distances.
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