# Polynomial Graph Analysis## Graph DescriptionThe provided graph is of the polynomial function \( g(x) \). It displays a curve plotted on a Cartesian coordinate system with the x-axis ranging from -4 to 4 and the y-axis from -4 to 4.### Observations- **Roots**: The graph intersects the x-axis at several points, indicating the roots of the polynomial.- **Behavior at Roots**: The graph either crosses or touches the x-axis at each root, suggesting their multiplicities (odd or even).- **End Behavior**: The graph starts in the lower-left quadrant and ends in the lower-right quadrant, indicating the sign of the leading coefficient.## Instructions1. **List the Roots of \( g \) and Determine Their Multiplicities:** - Root: \( x = \_ \) Multiplicity: ODD / EVEN - Root: \( x = \_ \) Multiplicity: ODD / EVEN - Root: \( x = \_ \) Multiplicity: ODD / EVEN - Root: \( x = \_ \) Multiplicity: ODD / EVEN2. **Determine the Leading Coefficient:** - Circle the correct answer: Is the leading coefficient of \( g \) positive or negative? - Leading coefficient: POSITIVE / NEGATIVE3. **Determine the Degree of \( g \):** - Circle the correct answer: Is the degree of \( g \) odd or even? - Degree: ODD / EVEN## Graph Analysis- **Root Analysis**: Identify where \( g(x) = 0 \). Check if the graph crosses (odd multiplicity) or touches (even multiplicity) the x-axis.- **Leading Coefficient**: Observing if the ends of the graph point in opposite directions (odd degree) or the same direction (even degree) will indicate the leading coefficient's sign.- **Degree**: Analyze the graph’s end behavior to determine if the polynomial has an odd or even degree.Use this information to complete the tasks above and gain a deeper understanding of polynomial characteristics and behaviors as represented by their graphs.

In this question we will use basic of calculus i.e concept of reading of graph. We will simply…

-4 -3 -2 -1 3 -2 -3 List the roots of g and circle the correct answer whether their multiplicities are odd or ever root: x = multiplicity: ODD / EVEN root: x = multiplicity: ODD / EVEN multiplicity: ODD / EVEN root: x = multiplicity: ODD / EVEN root: x = Circle the correct answer: Is the leading coefficient of g positive or negative? Leading coefficient: POSITIVE / NEGATIVE Circle the correct answer: Is the degree of g odd or even? Degree: ODD / EVEN

-4 -3 -2 -1 3 -2 -3 List the roots of g and circle the correct answer whether their multiplicities are odd or ever root: x = multiplicity: ODD / EVEN root: x = multiplicity: ODD / EVEN multiplicity: ODD / EVEN root: x = multiplicity: ODD / EVEN root: x = Circle the correct answer: Is the leading coefficient of g positive or negative? Leading coefficient: POSITIVE / NEGATIVE Circle the correct answer: Is the degree of g odd or even? Degree: ODD / EVEN

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

# Polynomial Graph Analysis

## Graph Description

The provided graph is of the polynomial function \( g(x) \). It displays a curve plotted on a Cartesian coordinate system with the x-axis ranging from -4 to 4 and the y-axis from -4 to 4.

### Observations

- **Roots**: The graph intersects the x-axis at several points, indicating the roots of the polynomial.
- **Behavior at Roots**: The graph either crosses or touches the x-axis at each root, suggesting their multiplicities (odd or even).
- **End Behavior**: The graph starts in the lower-left quadrant and ends in the lower-right quadrant, indicating the sign of the leading coefficient.

## Instructions

1. **List the Roots of \( g \) and Determine Their Multiplicities:**
- Root: \( x = \_ \)      Multiplicity: ODD / EVEN
- Root: \( x = \_ \)      Multiplicity: ODD / EVEN
- Root: \( x = \_ \)      Multiplicity: ODD / EVEN
- Root: \( x = \_ \)      Multiplicity: ODD / EVEN

2. **Determine the Leading Coefficient:**
- Circle the correct answer: Is the leading coefficient of \( g \) positive or negative?
- Leading coefficient: POSITIVE / NEGATIVE

3. **Determine the Degree of \( g \):**
- Circle the correct answer: Is the degree of \( g \) odd or even?
- Degree: ODD / EVEN

## Graph Analysis

- **Root Analysis**: Identify where \( g(x) = 0 \). Check if the graph crosses (odd multiplicity) or touches (even multiplicity) the x-axis.
- **Leading Coefficient**: Observing if the ends of the graph point in opposite directions (odd degree) or the same direction (even degree) will indicate the leading coefficient's sign.
- **Degree**: Analyze the graph’s end behavior to determine if the polynomial has an odd or even degree.

Use this information to complete the tasks above and gain a deeper understanding of polynomial characteristics and behaviors as represented by their graphs.

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