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

Level 1

The topics in this unit focus on understanding the end behaviour of a polynomial function from graphs and equations. 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} &= -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 \\
2
A LaTex expression showing \begin{align*}\text{highest power} &= 5\\ \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 \\
3
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 \\
4
A LaTex expression showing \begin{align*}\text{highest power} &= 4\\ \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 \\
5
A LaTex expression showing \begin{align*}\text{highest power} &= 7\\ \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 \\
6
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 \\
7
A LaTex expression showing \begin{align*}\text{highest power} &= 4\\ \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 \\
8
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 \\