Please answer the following problem. Thank you ### Problem 1: Graphing a Polynomial Function**Problem Statement:**Let \( f(x) = x^4 - x^3 - 6x^2 \). Sketch a graph of the function. Label all zeros and asymptotes on the graph, if they exist.**Steps to Solve:**1. **Determine the Zeros of the Function:** - To find the zeros of \( f(x) \), set \( f(x) = 0 \): \[ x^4 - x^3 - 6x^2 = 0 \] - Factor the equation: \[ x^2 (x^2 - x - 6) = 0 \] - Further factor \( x^2 - x - 6 \): \[ x^2 (x - 3)(x + 2) = 0 \] - The zeros are \( x = 0 \), \( x = 3 \), and \( x = -2 \).2. **Determine the Behavior at Infinity:** - As \( x \to \infty \), the highest degree term \( x^4 \) dictates that \( f(x) \to \infty \). - As \( x \to -\infty \), \( f(x) \to \infty \) because \( x^4 \) is an even degree polynomial.3. **Identify and Label Asymptotes:** - Polynomial functions do not have vertical or horizontal asymptotes, so there are none to label.4. **Sketch the Graph:** - Plot the zeros: \( (0,0) \), \( (3,0) \), \( (-2,0) \). - Determine the function's behavior at these points and in between them, considering the factors and higher-order terms.By following these steps, you can create an accurate sketch of the quadratic polynomial function and appropriately label any critical points.> **Note for Educators:**> Ensure that students understand the process of finding zeros and their significance in the function. Encourage the use of graphing tools or software to visualize the function.

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Answered: 1. Let f(x)=x-x-6x². Sketch a graph of…

1. Let f(x)=x-x-6x². Sketch a graph of the function. Label all zeros and asymptotes on the graph, if they exist.

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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