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

Level 1

This math topic focuses on understanding the end behavior of polynomial functions by examining their highest powers and leading coefficients. The problems require analyzing polynomials to determine if the leading coefficient is positive or negative and if the degree of the polynomial (highest power) is even or odd. This helps to predict the function's behavior as the input values approach infinity or negative infinity. Each question provides a pair of possible descriptions, and students need to choose the correct one based on the given polynomial's characteristics.

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 Rule Worksheet

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Function End Behaviour (Polynomials) - Power and Coefficient to Rule
1
A LaTex expression showing \begin{align*}\text{highest power} &= 3\\ \text{leading coefficient} &= -2\end{align*}
How would this highest power and leading coefficient be described when analyzing end behaviour?
a A LaTex expression showing \begin{align*}\text{highest power} &= \text{odd}\\ \text{leading coefficient} &= \text{positive}\end{align*}
b A LaTex expression showing \begin{align*}\text{highest power} &= \text{odd}\\ \text{leading coefficient} &= \text{negative}\end{align*}
2
A LaTex expression showing \begin{align*}\text{highest power} &= 5\\ \text{leading coefficient} &= 5\end{align*}
How would this highest power and leading coefficient be described when analyzing end behaviour?
a A LaTex expression showing \begin{align*}\text{highest power} &= \text{odd}\\ \text{leading coefficient} &= \text{positive}\end{align*}
b A LaTex expression showing \begin{align*}\text{highest power} &= \text{even}\\ \text{leading coefficient} &= \text{positive}\end{align*}
3
A LaTex expression showing \begin{align*}\text{highest power} &= 1\\ \text{leading coefficient} &= -3\end{align*}
How would this highest power and leading coefficient be described when analyzing end behaviour?
a A LaTex expression showing \begin{align*}\text{highest power} &= \text{even}\\ \text{leading coefficient} &= \text{negative}\end{align*}
b A LaTex expression showing \begin{align*}\text{highest power} &= \text{odd}\\ \text{leading coefficient} &= \text{negative}\end{align*}
4
A LaTex expression showing \begin{align*}\text{highest power} &= 3\\ \text{leading coefficient} &= 3\end{align*}
How would this highest power and leading coefficient be described when analyzing end behaviour?
a A LaTex expression showing \begin{align*}\text{highest power} &= \text{odd}\\ \text{leading coefficient} &= \text{negative}\end{align*}
b A LaTex expression showing \begin{align*}\text{highest power} &= \text{odd}\\ \text{leading coefficient} &= \text{positive}\end{align*}
5
A LaTex expression showing \begin{align*}\text{highest power} &= 7\\ \text{leading coefficient} &= 5\end{align*}
How would this highest power and leading coefficient be described when analyzing end behaviour?
a A LaTex expression showing \begin{align*}\text{highest power} &= \text{odd}\\ \text{leading coefficient} &= \text{positive}\end{align*}
b A LaTex expression showing \begin{align*}\text{highest power} &= \text{odd}\\ \text{leading coefficient} &= \text{negative}\end{align*}
6
A LaTex expression showing \begin{align*}\text{highest power} &= 4\\ \text{leading coefficient} &= -5\end{align*}
How would this highest power and leading coefficient be described when analyzing end behaviour?
a A LaTex expression showing \begin{align*}\text{highest power} &= \text{even}\\ \text{leading coefficient} &= \text{positive}\end{align*}
b A LaTex expression showing \begin{align*}\text{highest power} &= \text{even}\\ \text{leading coefficient} &= \text{negative}\end{align*}
7
A LaTex expression showing \begin{align*}\text{highest power} &= 3\\ \text{leading coefficient} &= 5\end{align*}
How would this highest power and leading coefficient be described when analyzing end behaviour?
a A LaTex expression showing \begin{align*}\text{highest power} &= \text{even}\\ \text{leading coefficient} &= \text{positive}\end{align*}
b A LaTex expression showing \begin{align*}\text{highest power} &= \text{odd}\\ \text{leading coefficient} &= \text{positive}\end{align*}
8
A LaTex expression showing \begin{align*}\text{highest power} &= 4\\ \text{leading coefficient} &= -2\end{align*}
How would this highest power and leading coefficient be described when analyzing end behaviour?
a A LaTex expression showing \begin{align*}\text{highest power} &= \text{even}\\ \text{leading coefficient} &= \text{negative}\end{align*}
b A LaTex expression showing \begin{align*}\text{highest power} &= \text{odd}\\ \text{leading coefficient} &= \text{negative}\end{align*}