You are asked to graph the given polynomial. Because the polynomial does not factor, you will have to use the material you learn in section 3.4 to find the zeroes. That will give you your x-intercepts. Combine this with the information on section 3.2, dealing with graphing polynomials. Be sure to mark enough points to make the graph as accurate as possible. Because this could just be graphed online, the graph is NOT the most important part of your grade. I will be grading your work. Be sure to show ALL work for the following: 1) List all possible zeroes and characteristics of them ( 2) Show work for testing the zeroes until you find all of the zeroes (x intercepts) and their multiplicity Give the exact value of the x intercepts. HINT: They are not all integers. You will have some irrational zeroes. V 3) Show your work for finding the y intercept ( 4) Show the end behavior and your reasoning for that end behavior. 5) With all of the above work done, you will then be able to mark appropriate points and connect them with a good sketch. Worksheet: Section 3.4 Activity to Graph.pdf
You are asked to graph the given polynomial. Because the polynomial does not factor, you will have to use the material you learn in section 3.4 to find the zeroes. That will give you your x-intercepts. Combine this with the information on section 3.2, dealing with graphing polynomials. Be sure to mark enough points to make the graph as accurate as possible. Because this could just be graphed online, the graph is NOT the most important part of your grade. I will be grading your work. Be sure to show ALL work for the following: 1) List all possible zeroes and characteristics of them ( 2) Show work for testing the zeroes until you find all of the zeroes (x intercepts) and their multiplicity Give the exact value of the x intercepts. HINT: They are not all integers. You will have some irrational zeroes. V 3) Show your work for finding the y intercept ( 4) Show the end behavior and your reasoning for that end behavior. 5) With all of the above work done, you will then be able to mark appropriate points and connect them with a good sketch. Worksheet: Section 3.4 Activity to Graph.pdf
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
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#### Detailed Notes:
- **Zeroes and Characteristics:** Include steps for applying the Rational Root Theorem, synthetic division, or other relevant methods.
- **Finding Zeroes:** Detail out the intermediate steps involved in solving the polynomial equations.
- **Y-Intercept Calculation:** Clearly demonstrate the substitution process.
- **End Behavior Analysis:** Describe how the degree and leading coefficient of the polynomial influence the graph's far-left and far-right behavior.
This guide aims to help students develop a thorough understanding of polynomial graphing by working through both theoretical and practical aspects of the process.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F55d38b4a-bd6a-41ed-9171-a3a35226d6fd%2Fa31072d7-e321-4465-a20a-d6441c8679b2%2F3nja6y6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Graphing Polynomials - Educational Guide
You are asked to graph the given polynomial. Because the polynomial does not factor, you will have to use the material you learn in Section 3.4 to find the zeroes. That will give you your x-intercepts. Combine this with the information on Section 3.2, dealing with graphing polynomials. **Be sure to mark enough points to make the graph as accurate as possible.**
Because this could just be graphed online, the graph is **NOT** the most important part of your grade. **I will be grading your work. Be sure to show ALL work for the following:**
1. **List all possible zeroes and characteristics of them** (e.g., whether they are real or complex, and their multiplicity).
2. **Show work for testing the zeroes until you find all of the zeroes (x-intercepts) and their multiplicity**.
- **Give the exact value of the x-intercepts.**
- **HINT:** They are not all integers. You will have some irrational zeroes.
3. **Show your work for finding the y-intercept** (e.g., substitute \( x = 0 \) into the polynomial).
4. **Show the end behavior and your reasoning for that end behavior** (e.g., based on the leading term of the polynomial).
5. **With all of the above work done, you will then be able to mark appropriate points and connect them with a good sketch.**
Worksheet: [Section 3.4 Activity to Graph.pdf](#)
---
#### Detailed Notes:
- **Zeroes and Characteristics:** Include steps for applying the Rational Root Theorem, synthetic division, or other relevant methods.
- **Finding Zeroes:** Detail out the intermediate steps involved in solving the polynomial equations.
- **Y-Intercept Calculation:** Clearly demonstrate the substitution process.
- **End Behavior Analysis:** Describe how the degree and leading coefficient of the polynomial influence the graph's far-left and far-right behavior.
This guide aims to help students develop a thorough understanding of polynomial graphing by working through both theoretical and practical aspects of the process.
![### Graphing Polynomial Functions
#### Instructions for Graphing a Given Polynomial
**Step-by-Step Guide:**
1. **Refer to Section 3.2:** Follow the steps outlined in this section for graphing polynomial functions.
2. **Important Note:** The given polynomial does NOT factor. Therefore, ensure to incorporate techniques from Section 3.4 on finding zeros of a polynomial.
You will need the zeros to graph the x-intercepts accurately.
#### Polynomial to Graph
\[ f(x) = x^4 - 3x^3 - 20x^2 - 24x - 8 \]
#### Explanation of the Graph
Below the given polynomial equation, a grid is provided on which the polynomial function will be graphically represented. The grid includes coordinate axes, labeled as \( x \) (horizontal axis) and \( y \) (vertical axis), and is split into equal squares for precise plotting.
**Graph Description Details:**
- **Coordinate Axes:** An \( x \)-axis (horizontal) and \( y \)-axis (vertical) intersect at the origin (0,0).
- **Grid Lines:** The grid divides the plane into small squares to aid in accurate plotting.
- **Arrows:** The arrows on the axes indicate the positive direction for both \( x \) and \( y \).
**Graphing Tips:**
- Begin by identifying and plotting the zeros of the polynomial to determine the \( x \)-intercepts.
- Evaluate the polynomial at various \( x \)-values to get corresponding \( y \)-values.
- Plot the points on the grid and connect them smoothly capturing the shape of the polynomial curve.
Refer to the polynomial graphing instructions in your textbook for more details and examples.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F55d38b4a-bd6a-41ed-9171-a3a35226d6fd%2Fa31072d7-e321-4465-a20a-d6441c8679b2%2Fuujrdq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Graphing Polynomial Functions
#### Instructions for Graphing a Given Polynomial
**Step-by-Step Guide:**
1. **Refer to Section 3.2:** Follow the steps outlined in this section for graphing polynomial functions.
2. **Important Note:** The given polynomial does NOT factor. Therefore, ensure to incorporate techniques from Section 3.4 on finding zeros of a polynomial.
You will need the zeros to graph the x-intercepts accurately.
#### Polynomial to Graph
\[ f(x) = x^4 - 3x^3 - 20x^2 - 24x - 8 \]
#### Explanation of the Graph
Below the given polynomial equation, a grid is provided on which the polynomial function will be graphically represented. The grid includes coordinate axes, labeled as \( x \) (horizontal axis) and \( y \) (vertical axis), and is split into equal squares for precise plotting.
**Graph Description Details:**
- **Coordinate Axes:** An \( x \)-axis (horizontal) and \( y \)-axis (vertical) intersect at the origin (0,0).
- **Grid Lines:** The grid divides the plane into small squares to aid in accurate plotting.
- **Arrows:** The arrows on the axes indicate the positive direction for both \( x \) and \( y \).
**Graphing Tips:**
- Begin by identifying and plotting the zeros of the polynomial to determine the \( x \)-intercepts.
- Evaluate the polynomial at various \( x \)-values to get corresponding \( y \)-values.
- Plot the points on the grid and connect them smoothly capturing the shape of the polynomial curve.
Refer to the polynomial graphing instructions in your textbook for more details and examples.
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