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
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.7: The Inverse Of A Matrix
Problem 33E
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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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