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Function End Behaviour (Polynomials) - Function to Behaviour

Level 1

This math topic focuses on understanding the end behavior of polynomial functions. Students are asked to determine how the outputs (y-values) of given polynomial functions behave as the inputs (x-values) approach positive or negative infinity. Each problem presents a different polynomial function, and students need to choose between two described behaviors that accurately reflect how the function's graph extends towards infinity. These problems help students grasp important concepts in polynomial functions and their asymptotic behaviors, foundational for calculus and higher-level mathematics.

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

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Function End Behaviour (Polynomials) - Function to Behaviour Worksheet

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Function End Behaviour (Polynomials) - Function to Behaviour
1
What end behaviour would this function have?
A LaTex expression showing f(x) = 2x to the power of 3 +3x to the power of 2 +3x
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 f(x) = -2x+2
What end behaviour would this function have?
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
What end behaviour would this function have?
A LaTex expression showing f(x) = -5x to the power of 7 -5x to the power of 6 -5x to the power of 5
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
What end behaviour would this function have?
A LaTex expression showing f(x) = 2x to the power of 3 -3x to the power of 2 -3x
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
What end behaviour would this function have?
A LaTex expression showing f(x) = -3x to the power of 4 -5x to the power of 3 -5x to the power of 2
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
What end behaviour would this function have?
A LaTex expression showing f(x) = 5x to the power of 3 -2x to the power of 2 -2x
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
What end behaviour would this function have?
A LaTex expression showing f(x) = 3x to the power of 6 +3x to the power of 5 +3x to the power of 4
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
What end behaviour would this function have?
A LaTex expression showing f(x) = -4x to the power of 5 +2x to the power of 4 +2x to the power of 3
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 \\