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Function End Behaviour (Polynomials) - Function to Rule

Level 1

This math topic focuses on understanding the end behavior of polynomial functions. Students analyze the degree and leading coefficient of given polynomial functions to determine their behavior as \( x \) approaches positive or negative infinity. The questions involve identifying whether the polynomial's highest power is odd or even, and if the leading coefficient is positive or negative, based on the provided polynomial expressions. This helps in predicting the direction the function will tend towards in both ends of the graph.

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 Rule Worksheet

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Function End Behaviour (Polynomials) - Function to Rule
1
What end behaviour criteria is correct for this function?
A LaTex expression showing f(x) = 2x to the power of 3 -5x to the power of 2 -5x
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*}
2
What end behaviour criteria is correct for this function?
A LaTex expression showing f(x) = 3x to the power of 2 -5x-5
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
What end behaviour criteria is correct for this function?
A LaTex expression showing f(x) = -2x to the power of 2 +4x+4
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{even}\\ \text{leading coefficient} &= \text{positive}\end{align*}
4
What end behaviour criteria is correct for this function?
A LaTex expression showing f(x) = 3x to the power of 2 -2x-2
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*}
5
What end behaviour criteria is correct for this function?
A LaTex expression showing f(x) = 5x to the power of 6 -3x to the power of 5 -3x to the power of 4
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{even}\\ \text{leading coefficient} &= \text{positive}\end{align*}
6
A LaTex expression showing f(x) = 3x+5
What end behaviour criteria is correct for this function?
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*}
7
A LaTex expression showing f(x) = -2x-2
What end behaviour criteria is correct for this function?
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*}
8
What end behaviour criteria is correct for this function?
A LaTex expression showing f(x) = 2x to the power of 2 +4x+4
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{even}\\ \text{leading coefficient} &= \text{positive}\end{align*}