Function End Behaviour (Polynomials) - Rule to Behaviour

Level 1

This math topic focuses on understanding the end behavior of polynomial functions based on their highest power and leading coefficient. It teaches how to predict whether the function's graph will rise or fall as $x$ approaches infinity ($\infty$) or negative infinity ($-\infty$). The problems apply rules associated with these coefficients and powers (odd or even, positive or negative) to determine the direction of the graph's tails at the extremes. Additionally, it offers multiple-choice questions to pick the correct end behavior for given polynomial characteristics.

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 Behaviour Worksheet

Function End Behaviour (Polynomials) - Rule to Behaviour

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

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 $A LaTex expression showing \text{as }x \rightarrow -\infty , y \rightarrow -\infty \\ \text{as }x \rightarrow \infty , y \rightarrow -\infty \\$

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

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 $A LaTex expression showing \text{as }x \rightarrow -\infty , y \rightarrow \infty \\ \text{as }x \rightarrow \infty , y \rightarrow \infty \\$

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

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 $A LaTex expression showing \text{as }x \rightarrow -\infty , y \rightarrow \infty \\ \text{as }x \rightarrow \infty , y \rightarrow -\infty \\$

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

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 $A LaTex expression showing \text{as }x \rightarrow -\infty , y \rightarrow \infty \\ \text{as }x \rightarrow \infty , y \rightarrow -\infty \\$