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...
Related questions
Question
Is this the graph of a function of \( x \)?
- [ ] No
- [ ] Yes
---
**Explanation of the Graph:**
The graph provided is a plot on a Cartesian coordinate system with the x-axis and y-axis ranging from \(-8\) to \(8\). There is a curve plotted on the graph, resembling an inverted parabola that opens downwards. The curve intersects the y-axis at approximately \(-4\) (where \( y = -4 \)) and extends between \( x = -2 \) and \( x = 2 \).
**How to Determine if this Graph is a Function:**
To determine if the graph is a function of \( x \), you can use the "Vertical Line Test." A graph represents a function if and only if no vertical line intersects the graph at more than one point.
Upon visual inspection, if you draw vertical lines through various points on the x-axis, you will notice that these lines intersect the curve at more than one point, specifically between \( x = -2 \) and \( x = 2 \).
Thus, since it fails the Vertical Line Test, this graph **is not** a function of \( x \).
---
**Interactive Component:**
- Make your selection based on the explanation above.
- [ ] No
- [ ] Yes
**Time Remaining: 01**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F22969543-4b1b-47a8-98d2-f1e5e1e74392%2F92cd4f96-7a20-42be-88da-fdeafbd3c1a1%2Fvm37dy_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Exercise: Determine if the Graph is a Function of x**
---
**Question:**
Determine if the graph is a function of \( x \).
Is this the graph of a function of \( x \)?
- [ ] No
- [ ] Yes
---
**Explanation of the Graph:**
The graph provided is a plot on a Cartesian coordinate system with the x-axis and y-axis ranging from \(-8\) to \(8\). There is a curve plotted on the graph, resembling an inverted parabola that opens downwards. The curve intersects the y-axis at approximately \(-4\) (where \( y = -4 \)) and extends between \( x = -2 \) and \( x = 2 \).
**How to Determine if this Graph is a Function:**
To determine if the graph is a function of \( x \), you can use the "Vertical Line Test." A graph represents a function if and only if no vertical line intersects the graph at more than one point.
Upon visual inspection, if you draw vertical lines through various points on the x-axis, you will notice that these lines intersect the curve at more than one point, specifically between \( x = -2 \) and \( x = 2 \).
Thus, since it fails the Vertical Line Test, this graph **is not** a function of \( x \).
---
**Interactive Component:**
- Make your selection based on the explanation above.
- [ ] No
- [ ] Yes
**Time Remaining: 01**
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