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5.) Sketch the graph. f(x) = x³ + x² – x +1 %3D

5.) Sketch the graph. f(x) = x³ + x² – x +1 %3D

Calculus: Early Transcendentals
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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Question
**Exercise 5: Sketch the Graph** **Function:** \[ f(x) = x^3 + x^2 - x + 1 \] **Instructions:** Sketch the graph of the function \( f(x) = x^3 + x^2 - x + 1 \). Consider key features such as intercepts, end behavior, and critical points.
Transcribed Image Text:**Exercise 5: Sketch the Graph** **Function:** \[ f(x) = x^3 + x^2 - x + 1 \] **Instructions:** Sketch the graph of the function \( f(x) = x^3 + x^2 - x + 1 \). Consider key features such as intercepts, end behavior, and critical points.
Expert Solution
Given

The graph of a polynomial of 3 degree has at most  2 turns and 3 intersections with the x-axis.

If the degree of a polynomial is odd then the positive coefficient of odd degree represents that the up branch of the polynomial is on the right side and the lower branch is on the left.

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