Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Strategy -Graphing a Polynomial Function 1. Check for symmetry of any type. a. f(-x) = f(x) => symmetric about the y-axis b. f(-x) = -f(x) => symmetric about the origin c. quadratic function => symmetric about x = 2. Find all real zeros of the polynomial function. (where does it cross the x-axis) 3. Determine the behavior at the corresponding x-intercepts. 4. Determine the behavior as x -> 00 and as x -> -00. look at the degree of the polynomial and the leading coefficient b. if degree is odd, the graph approaches opposite oo if degree is even, the graph approaches the same oo 5. Calculate several ordered pairs including the y-intercept to verify your suspicions about the slope of the graph. 6. Draw a smooth curve through the points to make the graph. a. C. Graph the following function: f(x) = 6x – x³ – 25x² +4x+4

Strategy -Graphing a Polynomial Function 1. Check for symmetry of any type. a. f(-x) = f(x) => symmetric about the y-axis b. f(-x) = -f(x) => symmetric about the origin c. quadratic function => symmetric about x = 2. Find all real zeros of the polynomial function. (where does it cross the x-axis) 3. Determine the behavior at the corresponding x-intercepts. 4. Determine the behavior as x -> 00 and as x -> -00. look at the degree of the polynomial and the leading coefficient b. if degree is odd, the graph approaches opposite oo if degree is even, the graph approaches the same oo 5. Calculate several ordered pairs including the y-intercept to verify your suspicions about the slope of the graph. 6. Draw a smooth curve through the points to make the graph. a. C. Graph the following function: f(x) = 6x – x³ – 25x² +4x+4

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
100%
Show all work
**Strategy - Graphing a Polynomial Function** 1. **Check for symmetry of any type.** - \( f(-x) = f(x) \) ⇒ symmetric about the y-axis - \( f(-x) = -f(x) \) ⇒ symmetric about the origin - Quadratic function ⇒ symmetric about \( x = -b/(2a) \) 2. **Find all real zeros of the polynomial function** (where does it cross the x-axis). 3. **Determine the behavior at the corresponding x-intercepts.** 4. **Determine the behavior as \( x \to \infty \) and as \( x \to -\infty \).** - a. Look at the degree of the polynomial and the leading coefficient. - b. If the degree is odd, the graph approaches opposite \(\infty\). - c. If the degree is even, the graph approaches the same \(\infty\). 5. **Calculate several ordered pairs including the y-intercept to verify your suspicions about the slope of the graph.** 6. **Draw a smooth curve through the points to make the graph.** --- **Graph the following function:** \( f(x) = 6x^4 - x^3 - 25x^2 + 4x + 4 \) --- **Graph Description:** The graph is presented on a grid with axes ranging from -10 to 10 on both the x and y axes. The units are marked and divided into a decimal system for accurate plotting. Use this grid to plot the described polynomial function by following the six-step strategy mentioned above. The function \( f(x) = 6x^4 - x^3 - 25x^2 + 4x + 4 \) is a fourth-degree polynomial, which means its behavior at \( x \to \infty \) and \( x \to -\infty \) will approach the same infinity, due to the even degree. Start by finding real zeros and plot the intercepts, then sketch the curve by determining the behavior and connecting the points smoothly.
Transcribed Image Text:**Strategy - Graphing a Polynomial Function** 1. **Check for symmetry of any type.** - \( f(-x) = f(x) \) ⇒ symmetric about the y-axis - \( f(-x) = -f(x) \) ⇒ symmetric about the origin - Quadratic function ⇒ symmetric about \( x = -b/(2a) \) 2. **Find all real zeros of the polynomial function** (where does it cross the x-axis). 3. **Determine the behavior at the corresponding x-intercepts.** 4. **Determine the behavior as \( x \to \infty \) and as \( x \to -\infty \).** - a. Look at the degree of the polynomial and the leading coefficient. - b. If the degree is odd, the graph approaches opposite \(\infty\). - c. If the degree is even, the graph approaches the same \(\infty\). 5. **Calculate several ordered pairs including the y-intercept to verify your suspicions about the slope of the graph.** 6. **Draw a smooth curve through the points to make the graph.** --- **Graph the following function:** \( f(x) = 6x^4 - x^3 - 25x^2 + 4x + 4 \) --- **Graph Description:** The graph is presented on a grid with axes ranging from -10 to 10 on both the x and y axes. The units are marked and divided into a decimal system for accurate plotting. Use this grid to plot the described polynomial function by following the six-step strategy mentioned above. The function \( f(x) = 6x^4 - x^3 - 25x^2 + 4x + 4 \) is a fourth-degree polynomial, which means its behavior at \( x \to \infty \) and \( x \to -\infty \) will approach the same infinity, due to the even degree. Start by finding real zeros and plot the intercepts, then sketch the curve by determining the behavior and connecting the points smoothly.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 5 steps with 5 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS