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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text: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 = -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 -> 00 and as x -> -o0.
look at the degree of the polynomial and the leading coefficient
b. if degree is odd, the graph approaches opposite oo
C. 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.
Graph the following function: f(x) = 6x* – x³ – 25x² +4x+4
10
10-9-8-7-6-5 -4 -3-2 -1
10
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