Consider the function P(x) = (x – 2)°(x – 6) - The y-intercept is the point (0,-24) The x-intercept(s) is/are the point(s) (2,0).(6,0) As x → ∞, y → As x → 0, y →
Consider the function P(x) = (x – 2)°(x – 6) - The y-intercept is the point (0,-24) The x-intercept(s) is/are the point(s) (2,0).(6,0) As x → ∞, y → As x → 0, y →
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
![### Function Analysis
Consider the function \( P(x) = (x - 2)^2(x - 6) \).
#### Intercepts
- **Y-intercept**: The function crosses the y-axis at the point \((0, -24)\).
- **X-intercepts**: The function crosses the x-axis at the points \((2, 0)\) and \((6, 0)\).
#### End Behavior
- As \( x \to \infty \), \( y \to \) [Description needed here].
- As \( x \to -\infty \), \( y \to \) [Description needed here].
These elements give a comprehensive view of the function's behavior, focusing on intercepts and its behavior as \( x \) approaches infinity in both positive and negative directions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1d00c952-2041-4a5c-9ba9-d692090aff1e%2F112dfc93-a2d3-4148-8c2b-5b9f872ee7aa%2Ffx4lhna_processed.png&w=3840&q=75)
Transcribed Image Text:### Function Analysis
Consider the function \( P(x) = (x - 2)^2(x - 6) \).
#### Intercepts
- **Y-intercept**: The function crosses the y-axis at the point \((0, -24)\).
- **X-intercepts**: The function crosses the x-axis at the points \((2, 0)\) and \((6, 0)\).
#### End Behavior
- As \( x \to \infty \), \( y \to \) [Description needed here].
- As \( x \to -\infty \), \( y \to \) [Description needed here].
These elements give a comprehensive view of the function's behavior, focusing on intercepts and its behavior as \( x \) approaches infinity in both positive and negative directions.
Expert Solution
Step 1
Recall:
- The x intercept is the point where the line crosses the x axis .At this point y=0.
- The y intercept is the point where the line crosses the y-axis. At this point x=0.
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