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
![**Instruction:**
Factor to find all x-intercepts of the function.
**Function:**
\[ f(x) = x^2 - 2x + 1 \]
**Explanation:**
To find the x-intercepts of the function given by \( f(x) = x^2 - 2x + 1 \), factor the quadratic equation. Look for two numbers that multiply to +1 (the constant term) and add to -2 (the coefficient of x). The factored form is:
\[ f(x) = (x - 1)(x - 1) \]
Setting it to zero gives:
\[ (x - 1)^2 = 0 \]
Thus, the x-intercept is at:
\[ x = 1 \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8cc14db3-0b21-46fc-8a3d-1d0dbc6bee86%2F12a335d5-6ff4-4e55-85a9-0d8e1e433cec%2Fkjm21xp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Instruction:**
Factor to find all x-intercepts of the function.
**Function:**
\[ f(x) = x^2 - 2x + 1 \]
**Explanation:**
To find the x-intercepts of the function given by \( f(x) = x^2 - 2x + 1 \), factor the quadratic equation. Look for two numbers that multiply to +1 (the constant term) and add to -2 (the coefficient of x). The factored form is:
\[ f(x) = (x - 1)(x - 1) \]
Setting it to zero gives:
\[ (x - 1)^2 = 0 \]
Thus, the x-intercept is at:
\[ x = 1 \]
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