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,...
icon
Related questions
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.
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.
Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education