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Function End Behaviour (Polynomials) - Behaviour to Function

Level 1

This math topic focuses on the end behavior of polynomial functions. Specifically, students learn to match descriptions of end behaviors with their corresponding polynomial functions by analyzing the powers and coefficients of those functions. The problems involve determining which polynomial exhibits a specific asymptotic behavior as \(x\) approaches infinity or negative infinity. Each question presents a verbal or graphical description of a function's end behavior, and students must select the function that matches this description from given options. The questions cover a range of polynomial degrees and configurations.

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

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Function End Behaviour (Polynomials) - Behaviour to Function Worksheet

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Function End Behaviour (Polynomials) - Behaviour to Function
1
Which function (based on its powers and coefficents) would have this end behaviour?
A LaTex expression showing \text{as }x \rightarrow -\infty , y \rightarrow -\infty \\ \text{as }x \rightarrow \infty , y \rightarrow -\infty \\
a A LaTex expression showing f(x) = 5x to the power of 2 +3x+3
b A LaTex expression showing f(x) = -5x to the power of 2 +3x+3
2
Which function (based on its powers and coefficents) would have this end behaviour?
A LaTex expression showing \text{as }x \rightarrow -\infty , y \rightarrow \infty \\ \text{as }x \rightarrow \infty , y \rightarrow \infty \\
a A LaTex expression showing f(x) = 4x to the power of 3 -5x to the power of 2 -5x
b A LaTex expression showing f(x) = 4x to the power of 2 -5x-5
3
Which function (based on its powers and coefficents) would have this end behaviour?
A LaTex expression showing \text{as }x \rightarrow -\infty , y \rightarrow \infty \\ \text{as }x \rightarrow \infty , y \rightarrow -\infty \\
a A LaTex expression showing f(x) = -5x to the power of 5 +3x to the power of 4 +3x to the power of 3
b A LaTex expression showing f(x) = 5x to the power of 5 +3x to the power of 4 +3x to the power of 3
4
Which function (based on its powers and coefficents) would have this end behaviour?
A LaTex expression showing \text{as }x \rightarrow -\infty , y \rightarrow -\infty \\ \text{as }x \rightarrow \infty , y \rightarrow \infty \\
a A LaTex expression showing f(x) = 3x to the power of 4 +5x to the power of 3 +5x to the power of 2
b A LaTex expression showing f(x) = 3x to the power of 5 +5x to the power of 4 +5x to the power of 3