3. Which of the following would be the leading coefficient of \( f(x)=6-x+7 x^{2} \) ? \( \begin{array}{ll}\text { (1) }-1 & \text { (3) } 7 \\ \text { (2) } 6 & \text { (4) }-7\end{array} \)

The leading coefficient of a polynomial is the coefficient of the term with the highest degree. In the function \( f(x) = 6 - x + 7x^{2} \), the term with the highest degree is \( 7x^{2} \). Therefore, the leading coefficient is \( 7 \). So, the answer is (3) 7. Another interesting fact is that leading coefficients can significantly influence the behavior of polynomials, especially as \( x \) approaches positive or negative infinity. A positive leading coefficient means the graph will rise to the right, while a negative one means it will fall. Remember, the degree of the polynomial also plays a crucial role in determining the graph's shape!