Given the function P(x) = x(x-2)(x+3), find its y-intercept: (0,0) its x-intercepts: (-3,0),(0,0), (2,0) x (unmatched parens syntax incomplete. (unmatched parens). syntax incomplete. (un (unmatched parens). syntax incomplete. (unmatched parens). sy When → ∞, y →∞0 When X Invalid use of a →-∞, y → 0⁰0 ✓
Given the function P(x) = x(x-2)(x+3), find its y-intercept: (0,0) its x-intercepts: (-3,0),(0,0), (2,0) x (unmatched parens syntax incomplete. (unmatched parens). syntax incomplete. (un (unmatched parens). syntax incomplete. (unmatched parens). sy When → ∞, y →∞0 When X Invalid use of a →-∞, y → 0⁰0 ✓
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 Functions: Analyzed Example**
### Given the function
\[ P(x) = x(x - 2)(x + 3), \]
find:
#### 1. The y-intercept:
When you substitute \( x = 0 \) into the polynomial \( P(x) \), the output value, which is the y-intercept, is:
\[ (0,0) \]
However, an error message indicates "Invalid use of a box."
#### 2. The x-intercepts:
Find the values of \( x \) where \( P(x) = 0 \). The x-intercepts are the solutions to the equation:
\[ x(x - 2)(x + 3) = 0 \]
The solutions are:
\[ (-3,0), (0,0), (2,0) \]
However, an error message indicates "syntax incomplete (unmatched parens)."
#### 3. End Behavior:
Analyze the end behavior of the polynomial function as \( x \) approaches positive and negative infinity.
- When \( x \to \infty \), \( y \to \infty \) ✓
- When \( x \to -\infty \), \( y \to -\infty \) ✓
The diagram illustrates valid checkmarks for both conditions.
---
**Explanation of Graphs/Diagrams:**
The text includes representations of the function’s intercepts and end behavior conditions. There are no explicit graphs or complex diagrams included, but rather textual and symbolic representations for the analysis. The visual marks (cross or checkmarks) indicate the correctness of the associated values or conditions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa5178d97-debf-4e38-84bd-a0fb36219423%2F62b92d70-108b-417c-b277-5b593bc0f335%2Ffwbrp2f_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Polynomial Functions: Analyzed Example**
### Given the function
\[ P(x) = x(x - 2)(x + 3), \]
find:
#### 1. The y-intercept:
When you substitute \( x = 0 \) into the polynomial \( P(x) \), the output value, which is the y-intercept, is:
\[ (0,0) \]
However, an error message indicates "Invalid use of a box."
#### 2. The x-intercepts:
Find the values of \( x \) where \( P(x) = 0 \). The x-intercepts are the solutions to the equation:
\[ x(x - 2)(x + 3) = 0 \]
The solutions are:
\[ (-3,0), (0,0), (2,0) \]
However, an error message indicates "syntax incomplete (unmatched parens)."
#### 3. End Behavior:
Analyze the end behavior of the polynomial function as \( x \) approaches positive and negative infinity.
- When \( x \to \infty \), \( y \to \infty \) ✓
- When \( x \to -\infty \), \( y \to -\infty \) ✓
The diagram illustrates valid checkmarks for both conditions.
---
**Explanation of Graphs/Diagrams:**
The text includes representations of the function’s intercepts and end behavior conditions. There are no explicit graphs or complex diagrams included, but rather textual and symbolic representations for the analysis. The visual marks (cross or checkmarks) indicate the correctness of the associated values or conditions.
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