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

Level 1

This topic focuses on understanding the end behavior of polynomial functions by examining the relationships between the highest power and the leading coefficient of the polynomial. The problems direct students to identify the correct pair of highest power and leading coefficient based on the provided end behavior descriptions. Each problem presents a specific scenario with two potential sets of values for the highest power (odd or even) and the leading coefficient (positive or negative), and students must select the pair that matches the described end behavior. This exercise is part of an introductory unit on the end behaviors of functions.

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

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

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

$A LaTex expression showing \begin{align*}\text{highest power} &= \text{odd}\\ \text{leading coefficient} &= \text{positive}\end{align*}$

Which highest power and leading coefficient fits this end behaviour description?

a $A LaTex expression showing \begin{align*}\text{highest power} &= 2\\ \text{leading coefficient} &= 2\end{align*}$

b $A LaTex expression showing \begin{align*}\text{highest power} &= 1\\ \text{leading coefficient} &= 2\end{align*}$

$A LaTex expression showing \begin{align*}\text{highest power} &= \text{even}\\ \text{leading coefficient} &= \text{positive}\end{align*}$

Which highest power and leading coefficient fits this end behaviour description?

a $A LaTex expression showing \begin{align*}\text{highest power} &= 3\\ \text{leading coefficient} &= 5\end{align*}$

b $A LaTex expression showing \begin{align*}\text{highest power} &= 2\\ \text{leading coefficient} &= 5\end{align*}$

$A LaTex expression showing \begin{align*}\text{highest power} &= \text{even}\\ \text{leading coefficient} &= \text{negative}\end{align*}$

Which highest power and leading coefficient fits this end behaviour description?

a $A LaTex expression showing \begin{align*}\text{highest power} &= 2\\ \text{leading coefficient} &= 3\end{align*}$

b $A LaTex expression showing \begin{align*}\text{highest power} &= 2\\ \text{leading coefficient} &= -3\end{align*}$

$A LaTex expression showing \begin{align*}\text{highest power} &= \text{odd}\\ \text{leading coefficient} &= \text{negative}\end{align*}$

Which highest power and leading coefficient fits this end behaviour description?

a $A LaTex expression showing \begin{align*}\text{highest power} &= 8\\ \text{leading coefficient} &= -5\end{align*}$

b $A LaTex expression showing \begin{align*}\text{highest power} &= 7\\ \text{leading coefficient} &= -5\end{align*}$