**Match the Polynomial Function with Its Graph**This educational activity is designed to help students understand the relationship between polynomial functions and their graphical representations. Students will be given a set of polynomial functions and corresponding graphs. The objective is to correctly pair each function with its graph. This exercise will enhance students' ability to interpret the graphical behavior of polynomial functions, including key features such as intercepts, turning points, and end behavior. ### Graph Analysis and Function Identification#### Graph (g)- **Description**: This graph features a curve that starts high on the y-axis, dips steeply, and rises again. The curve exhibits an inflection point, where the concavity changes.- **Equation Options**: 1. $ f(x) = -2x + 1 $ 2. $ f(x) = -2x^2 - 9x $ 3. $ f(x) = -\frac{1}{4}x^4 + 5x^2 $ 4. $ f(x) = x^4 + 2x^3 $ 5. $ f(x) = x^2 - 5x $ 6. $ f(x) = 2x^3 - 3x + 3 $ (Correct Choice) 7. $ f(x) = -\frac{1}{3}x^3 + x^2 - \frac{4}{3} $ 8. $ f(x) = \frac{1}{5}x^5 - 2x^3 + \frac{9}{5}x $#### Graph (h)- **Description**: The graph is a downward-opening parabola. It starts at the top left, reaches a peak, and then descends on the right.- **Equation Options**: 1. $ f(x) = -2x + 1 $ 2. $ f(x) = -2x^2 - 9x $ (Correct Choice) 3. $ f(x) = -\frac{1}{4}x^4 + 5x^2 $ 4. $ f(x) = x^4 + 2x^3 $ 5. $ f(x) = x^2 - 5x $ 6. $ f(x) = 2x^3 - 3x + 3 $These graphs illustrate the behavior of different polynomial functions. By observing the characteristics of the graphs, such as turning points and general shape, one can match each graph to its corresponding function.

Name: **Match the Polynomial Function with Its Graph**This educational acti
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Description: **Match the Polynomial Function with Its Graph**This educational activity is designed to help students understand the relationship between polynomial functions and their graphical representations. Students will be given a set of polynomial functions

Math

Calculus

y 10- - 10 -5 5 10 -5 |-10| f(x) = -2x + 1 f(x) 3D —2x2 - 9х 1 + 5x2 4 f(x) f(x) = x4 + 2x3 %3D f(x) = x2 – 5x f(x) = 2x3 Зх + 3 f(x) 1,3 + x2 4 = - O f(x) = x5 - 2x3 + | (h) y 10F - 10 5 10 -5 -10 f(x) = = -2x + 1 f(x) %3D —2x2 — 9х

y 10- - 10 -5 5 10 -5 |-10| f(x) = -2x + 1 f(x) 3D —2x2 - 9х 1 + 5x2 4 f(x) f(x) = x4 + 2x3 %3D f(x) = x2 – 5x f(x) = 2x3 Зх + 3 f(x) 1,3 + x2 4 = - O f(x) = x5 - 2x3 + | (h) y 10F - 10 5 10 -5 -10 f(x) = = -2x + 1 f(x) %3D —2x2 — 9х

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

**Match the Polynomial Function with Its Graph**

This educational activity is designed to help students understand the relationship between polynomial functions and their graphical representations. Students will be given a set of polynomial functions and corresponding graphs. The objective is to correctly pair each function with its graph. This exercise will enhance students' ability to interpret the graphical behavior of polynomial functions, including key features such as intercepts, turning points, and end behavior.

### Graph Analysis and Function Identification

#### Graph (g)
- **Description**: This graph features a curve that starts high on the y-axis, dips steeply, and rises again. The curve exhibits an inflection point, where the concavity changes.
- **Equation Options**:
1. $ f(x) = -2x + 1 $
2. $ f(x) = -2x^2 - 9x $
3. $ f(x) = -\frac{1}{4}x^4 + 5x^2 $
4. $ f(x) = x^4 + 2x^3 $
5. $ f(x) = x^2 - 5x $
6. $ f(x) = 2x^3 - 3x + 3 $ (Correct Choice)
7. $ f(x) = -\frac{1}{3}x^3 + x^2 - \frac{4}{3} $
8. $ f(x) = \frac{1}{5}x^5 - 2x^3 + \frac{9}{5}x $

#### Graph (h)
- **Description**: The graph is a downward-opening parabola. It starts at the top left, reaches a peak, and then descends on the right.
- **Equation Options**:
1. $ f(x) = -2x + 1 $
2. $ f(x) = -2x^2 - 9x $ (Correct Choice)
3. $ f(x) = -\frac{1}{4}x^4 + 5x^2 $
4. $ f(x) = x^4 + 2x^3 $
5. $ f(x) = x^2 - 5x $
6. $ f(x) = 2x^3 - 3x + 3 $

These graphs illustrate the behavior of different polynomial functions. By observing the characteristics of the graphs, such as turning points and general shape, one can match each graph to its corresponding function.

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