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Function End Behaviour (Polynomials) - Power and Coefficient to Behaviour

Level 1

This math topic focuses on understanding the end behavior of polynomial functions based on their leading coefficient and highest power. Questions prompt learners to deduce how polynomials will behave as \( x \) approaches infinity or negative infinity. Each problem presents a polynomial characterized by its highest power and leading coefficient, and students choose which behavior description fits the polynomial's characteristics. This exercise is foundational for grasping how polynomial functions behave at extreme values of \( x \).

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Function End Behaviour (Polynomials) - Power and Coefficient to Behaviour Worksheet

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Function End Behaviour (Polynomials) - Power and Coefficient to Behaviour
1
A LaTex expression showing \begin{align*}\text{highest power} &= 6\\ \text{leading coefficient} &= -2\end{align*}
What end behaviour would this power and coefficient create?
a A LaTex expression showing \text{as }x \rightarrow -\infty , y \rightarrow -\infty \\ \text{as }x \rightarrow \infty , y \rightarrow -\infty \\
b A LaTex expression showing \text{as }x \rightarrow -\infty , y \rightarrow \infty \\ \text{as }x \rightarrow \infty , y \rightarrow \infty \\
2
A LaTex expression showing \begin{align*}\text{highest power} &= 1\\ \text{leading coefficient} &= -2\end{align*}
What end behaviour would this power and coefficient create?
a A LaTex expression showing \text{as }x \rightarrow -\infty , y \rightarrow -\infty \\ \text{as }x \rightarrow \infty , y \rightarrow \infty \\
b A LaTex expression showing \text{as }x \rightarrow -\infty , y \rightarrow \infty \\ \text{as }x \rightarrow \infty , y \rightarrow -\infty \\
3
A LaTex expression showing \begin{align*}\text{highest power} &= 3\\ \text{leading coefficient} &= -2\end{align*}
What end behaviour would this power and coefficient create?
a A LaTex expression showing \text{as }x \rightarrow -\infty , y \rightarrow \infty \\ \text{as }x \rightarrow \infty , y \rightarrow -\infty \\
b A LaTex expression showing \text{as }x \rightarrow -\infty , y \rightarrow -\infty \\ \text{as }x \rightarrow \infty , y \rightarrow -\infty \\
4
A LaTex expression showing \begin{align*}\text{highest power} &= 7\\ \text{leading coefficient} &= -5\end{align*}
What end behaviour would this power and coefficient create?
a A LaTex expression showing \text{as }x \rightarrow -\infty , y \rightarrow \infty \\ \text{as }x \rightarrow \infty , y \rightarrow -\infty \\
b A LaTex expression showing \text{as }x \rightarrow -\infty , y \rightarrow -\infty \\ \text{as }x \rightarrow \infty , y \rightarrow \infty \\
5
A LaTex expression showing \begin{align*}\text{highest power} &= 6\\ \text{leading coefficient} &= 5\end{align*}
What end behaviour would this power and coefficient create?
a A LaTex expression showing \text{as }x \rightarrow -\infty , y \rightarrow \infty \\ \text{as }x \rightarrow \infty , y \rightarrow -\infty \\
b A LaTex expression showing \text{as }x \rightarrow -\infty , y \rightarrow \infty \\ \text{as }x \rightarrow \infty , y \rightarrow \infty \\
6
A LaTex expression showing \begin{align*}\text{highest power} &= 1\\ \text{leading coefficient} &= 3\end{align*}
What end behaviour would this power and coefficient create?
a A LaTex expression showing \text{as }x \rightarrow -\infty , y \rightarrow \infty \\ \text{as }x \rightarrow \infty , y \rightarrow -\infty \\
b A LaTex expression showing \text{as }x \rightarrow -\infty , y \rightarrow -\infty \\ \text{as }x \rightarrow \infty , y \rightarrow \infty \\
7
A LaTex expression showing \begin{align*}\text{highest power} &= 5\\ \text{leading coefficient} &= -3\end{align*}
What end behaviour would this power and coefficient create?
a A LaTex expression showing \text{as }x \rightarrow -\infty , y \rightarrow \infty \\ \text{as }x \rightarrow \infty , y \rightarrow -\infty \\
b A LaTex expression showing \text{as }x \rightarrow -\infty , y \rightarrow \infty \\ \text{as }x \rightarrow \infty , y \rightarrow \infty \\
8
A LaTex expression showing \begin{align*}\text{highest power} &= 1\\ \text{leading coefficient} &= -4\end{align*}
What end behaviour would this power and coefficient create?
a A LaTex expression showing \text{as }x \rightarrow -\infty , y \rightarrow \infty \\ \text{as }x \rightarrow \infty , y \rightarrow -\infty \\
b A LaTex expression showing \text{as }x \rightarrow -\infty , y \rightarrow -\infty \\ \text{as }x \rightarrow \infty , y \rightarrow \infty \\