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Determining the Graph Behavior of Polynomial Functions based on the Leading Term, Study notes of Algebra

Ross Medical Education CenterAlgebra

Instructions for identifying the degree and leading term of polynomial functions, and matching them to one of four possible graphs (a, b, c, or d) based on the sign of the leading term coefficient. Six examples are given for practice.

Typology: Study notes

2021/2022

Uploaded on 09/12/2022

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The Leading-Term Test
The theory states: If anxn is the leading term of a polynomial function, then the behavior of the graph as
x
and as
x 
can be described in one of the four following ways:
Degree Leading Degree Leading
Coefficient Coefficient
Even
Positive
A
Odd
Positive
C
Even
Negative
B
Odd
Negative
D
pf2

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The Leading-Term Test

The theory states: If anxn^ is the leading term of a polynomial function, then the behavior of the graph as x  and as

x   can be described in one of the four following ways:

Degree Leading Degree Leading Coefficient Coefficient

Even Positive

A

Odd Positive

C

Even Negative

B

Odd Negative

D

For the following functions, determine the degree of the function, the leading term coefficient, and match the functions to graph A, B, C, or D.

1. f ( ) x  6 x^2  2 x  3 Degree: Leading Term: Graph =

2. x^3^  3 Degree: Leading Term: Graph =

3. f ( ) x   x 3^  x^2  x  2 Degree: Leading Term: Graph =

4. f ( ) x   x^2  x  5 Degree: Leading Term: Graph =

5. f ( ) x   x 2  5 x  1 Degree: Leading Term: Graph =

6. f ( ) x   x^3  x  6 Degree: Leading Term: Graph =

Answers:

  1. Degree: Even Leading Term: Positive Graph = A
  2. Degree: Odd Leading Term: Positive Graph = C
  3. Degree: Odd Leading Term: Negative Graph = D
  4. Degree: Even Leading Term: Negative Graph = B
  5. Degree: Even Leading Term: Negative Graph = B
  6. Degree: Odd Leading Term: Negative Graph = D