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

Level 1

This math topic focuses on identifying the highest power and the leading coefficient of polynomial functions. Each question presents a polynomial function and asks to determine these two components. The functions vary in complexity, from single linear ones to higher-degree polynomials. This helps strengthen the fundamental understanding of polynomial function structure, crucial for analyzing their end behavior as part of a broader study on function behavior and characteristics.

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 Power and Coefficient Worksheet

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Function End Behaviour (Polynomials) - Function to Power and Coefficient
1
What is the highest power and leading coefficient of this function?
A LaTex expression showing f(x) = -2x to the power of 7 -3x to the power of 6 -3x to the power of 5
a A LaTex expression showing \begin{align*}\text{highest power} &= 7\\ \text{leading coefficient} &= -3\end{align*}
b A LaTex expression showing \begin{align*}\text{highest power} &= 7\\ \text{leading coefficient} &= -2\end{align*}
2
What is the highest power and leading coefficient of this function?
A LaTex expression showing f(x) = 5x to the power of 3 -4x to the power of 2 -4x
a A LaTex expression showing \begin{align*}\text{highest power} &= 3\\ \text{leading coefficient} &= 5\end{align*}
b A LaTex expression showing \begin{align*}\text{highest power} &= 3\\ \text{leading coefficient} &= -5\end{align*}
3
A LaTex expression showing f(x) = -3x+2
What is the highest power and leading coefficient of this function?
a A LaTex expression showing \begin{align*}\text{highest power} &= 1\\ \text{leading coefficient} &= -3\end{align*}
b A LaTex expression showing \begin{align*}\text{highest power} &= 1\\ \text{leading coefficient} &= 3\end{align*}
4
What is the highest power and leading coefficient of this function?
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 \begin{align*}\text{highest power} &= 7\\ \text{leading coefficient} &= 5\end{align*}
b A LaTex expression showing \begin{align*}\text{highest power} &= 7\\ \text{leading coefficient} &= -5\end{align*}
5
What is the highest power and leading coefficient of this function?
A LaTex expression showing f(x) = -5x to the power of 3 +2x to the power of 2 +2x
a A LaTex expression showing \begin{align*}\text{highest power} &= 3\\ \text{leading coefficient} &= 5\end{align*}
b A LaTex expression showing \begin{align*}\text{highest power} &= 3\\ \text{leading coefficient} &= -5\end{align*}
6
What is the highest power and leading coefficient of this function?
A LaTex expression showing f(x) = -4x to the power of 3 -2x to the power of 2 -2x
a A LaTex expression showing \begin{align*}\text{highest power} &= 3\\ \text{leading coefficient} &= 4\end{align*}
b A LaTex expression showing \begin{align*}\text{highest power} &= 3\\ \text{leading coefficient} &= -4\end{align*}
7
What is the highest power and leading coefficient of this function?
A LaTex expression showing f(x) = -2x to the power of 2 +5x+5
a A LaTex expression showing \begin{align*}\text{highest power} &= 2\\ \text{leading coefficient} &= -2\end{align*}
b A LaTex expression showing \begin{align*}\text{highest power} &= 1\\ \text{leading coefficient} &= -2\end{align*}
8
A LaTex expression showing f(x) = -4x-4
What is the highest power and leading coefficient of this function?
a A LaTex expression showing \begin{align*}\text{highest power} &= 1\\ \text{leading coefficient} &= -4\end{align*}
b A LaTex expression showing \begin{align*}\text{highest power} &= 1\\ \text{leading coefficient} &= 4\end{align*}