On your own paper, draw the graph of a function f(x) on [0,10] that has the following properties. Be sure to label your axes and draw as neatly as possible. Also, make sure your finished graph is actually a function! lim f(x) = ∞ А. x→2- В. x→2° lim f(x) = 2 %3D C. lim f(x) exists, but f(x) is not continuous at x = 4. x→4 D. f(x) has a jump discontinuity at x=6. E. lim f(x) does not exist. x→8
On your own paper, draw the graph of a function f(x) on [0,10] that has the following properties. Be sure to label your axes and draw as neatly as possible. Also, make sure your finished graph is actually a function! lim f(x) = ∞ А. x→2- В. x→2° lim f(x) = 2 %3D C. lim f(x) exists, but f(x) is not continuous at x = 4. x→4 D. f(x) has a jump discontinuity at x=6. E. lim f(x) does not exist. x→8
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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![### Instructions for Graphing a Function \( f(x) \) on an Interval \([0,10]\)
#### Objective:
Draw the graph of a function \( f(x) \) on the interval \([0,10]\) with the following specific properties. Ensure to label your axes and draw as neatly as possible. Verify that your finished graph satisfies the definition of a function.
#### Properties to Include in Your Graph:
1. **Property A:**
\[
\lim_{{x \to 2^-}} f(x) = \infty
\]
- The limit of \( f(x) \) as \( x \) approaches 2 from the left is infinity, indicating a vertical asymptote at \( x = 2 \) from the left side.
2. **Property B:**
\[
\lim_{{x \to 2^+}} f(x) = 2
\]
- The limit of \( f(x) \) as \( x \) approaches 2 from the right is 2.
3. **Property C:**
\[
\lim_{{x \to 4}} f(x) \text{ exists, but } f(x) \text{ is not continuous at } x = 4.
\]
- The limit of \( f(x) \) as \( x \) approaches 4 exists, however, \( f(x) \) itself is not continuous at \( x = 4 \). This suggests a removable discontinuity or a hole at \( x = 4 \).
4. **Property D:**
- \( f(x) \) has a jump discontinuity at \( x = 6 \).
- This means there is a sudden jump in the value of \( f(x) \) at \( x = 6 \).
5. **Property E:**
\[
\lim_{{x \to 8}} f(x) \text{ does not exist.}
\]
- The limit of \( f(x) \) as \( x \) approaches 8 does not exist, indicating a discontinuity at or around \( x = 8 \).
#### Steps to Draw the Graph:
1. **Axes and Scale:**
- Draw and label the x-axis from 0 to 10.
- Draw and label the y-axis with appropriate scale based on](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6bcaed0f-2f01-4310-ad37-5698e9f2c4bd%2F6def6390-88c8-4636-b4e0-8fab5b206aa8%2Fzdw9ehu.png&w=3840&q=75)
Transcribed Image Text:### Instructions for Graphing a Function \( f(x) \) on an Interval \([0,10]\)
#### Objective:
Draw the graph of a function \( f(x) \) on the interval \([0,10]\) with the following specific properties. Ensure to label your axes and draw as neatly as possible. Verify that your finished graph satisfies the definition of a function.
#### Properties to Include in Your Graph:
1. **Property A:**
\[
\lim_{{x \to 2^-}} f(x) = \infty
\]
- The limit of \( f(x) \) as \( x \) approaches 2 from the left is infinity, indicating a vertical asymptote at \( x = 2 \) from the left side.
2. **Property B:**
\[
\lim_{{x \to 2^+}} f(x) = 2
\]
- The limit of \( f(x) \) as \( x \) approaches 2 from the right is 2.
3. **Property C:**
\[
\lim_{{x \to 4}} f(x) \text{ exists, but } f(x) \text{ is not continuous at } x = 4.
\]
- The limit of \( f(x) \) as \( x \) approaches 4 exists, however, \( f(x) \) itself is not continuous at \( x = 4 \). This suggests a removable discontinuity or a hole at \( x = 4 \).
4. **Property D:**
- \( f(x) \) has a jump discontinuity at \( x = 6 \).
- This means there is a sudden jump in the value of \( f(x) \) at \( x = 6 \).
5. **Property E:**
\[
\lim_{{x \to 8}} f(x) \text{ does not exist.}
\]
- The limit of \( f(x) \) as \( x \) approaches 8 does not exist, indicating a discontinuity at or around \( x = 8 \).
#### Steps to Draw the Graph:
1. **Axes and Scale:**
- Draw and label the x-axis from 0 to 10.
- Draw and label the y-axis with appropriate scale based on
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