## Polynomial Function Analysis### 2. Given the function $ f(x) = -x^2(x - 3)(x - 1) $a. **Find the x and y-intercepts:**- **X-Intercepts:** Set $ f(x) = 0 $ and solve for $ x $.- **Y-Intercept:** Evaluate $ f(0) $.b. **Crosses or touches:**- Analyze which roots the polynomial crosses the x-axis and which ones it just touches.c. **End Behavior:**- Determine what happens to $ f(x) $ as $ x \rightarrow \infty $ and $ x \rightarrow -\infty $.d. **The Maximum Number of Turning Points:**- The degree of the polynomial gives the maximum number of turning points.e. **Intervals:**- Identify the intervals where the function is increasing or decreasing.f. **Graph:**- The diagram represents the coordinate plane with labeled axes.- **X-Axis:** Ranges from -4 to 4 with increments.- **Y-Axis:** Ranges from -50 to 100 with increments.Use this setup to sketch the graph of the polynomial function and analyze its behavior in detail.

Name: ## Polynomial Function Analysis### 2. Given the function $ f(x) = -x
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Description: ## Polynomial Function Analysis### 2. Given the function \( f(x) = -x^2(x - 3)(x - 1) $a. **Find the x and y-intercepts:**- **X-Intercepts:** Set $ f(x) = 0 $ and solve for $ x $.- **Y-Intercept:** Evaluate $ f(0) $.b. **Crosses or touches:**

Hey, since there are multiple sub-parts posted, we will answer the first 3 sub-parts. If you want…

Answered: 2. f(x) %3D — х? (х — 3) (х — 1) a.…

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2. f(x) %3D — х? (х — 3) (х — 1) a. Find the x and y – intercepts: b. crosses or touches : c. End behavior :

Advanced Engineering Mathematics

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ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

## Polynomial Function Analysis

### 2. Given the function $ f(x) = -x^2(x - 3)(x - 1) $

a. **Find the x and y-intercepts:**

- **X-Intercepts:** Set $ f(x) = 0 $ and solve for $ x $.
- **Y-Intercept:** Evaluate $ f(0) $.

b. **Crosses or touches:**
- Analyze which roots the polynomial crosses the x-axis and which ones it just touches.

c. **End Behavior:**
- Determine what happens to $ f(x) $ as $ x \rightarrow \infty $ and $ x \rightarrow -\infty $.

d. **The Maximum Number of Turning Points:**
- The degree of the polynomial gives the maximum number of turning points.

e. **Intervals:**
- Identify the intervals where the function is increasing or decreasing.

f. **Graph:**

- The diagram represents the coordinate plane with labeled axes.
- **X-Axis:** Ranges from -4 to 4 with increments.
- **Y-Axis:** Ranges from -50 to 100 with increments.

Use this setup to sketch the graph of the polynomial function and analyze its behavior in detail.

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