OF POLYNOMIAL FUNCTIONS Identify the degree, leading coefficient, zeros, end behavior, and create a sketch of the fu without the use of technology. (An accurate \( y \)-intercept is not needed for the sketch). Part 1 \( \begin{array}{ll}\text { (1) } p(r)=-2(r-1)(r+2)(r-2) & \text { (2.) } f(t)=3 t(t-3)(t+4)\end{array} \)

The first polynomial function, \( p(r) = -2(r-1)(r+2)(r-2) \), is a cubic polynomial. Its degree is 3, and the leading coefficient is -2, indicating it opens downwards. The zeros are found at \( r = 1, -2, \) and \( 2 \). For end behavior, as \( r \to -\infty \), \( p(r) \to \infty \) and as \( r \to \infty \), \( p(r) \to -\infty \). You can sketch a cubic function with these characteristics: starting high on the left, crossing the x-axis at the zeros, and ending low on the right. For the second polynomial function, \( f(t) = 3t(t-3)(t+4) \), it is also a cubic polynomial with degree 3 and a leading coefficient of 3, showing it opens upwards. The zeros here are at \( t = 0, 3, \) and \( -4 \). The end behavior is such that as \( t \to -\infty \), \( f(t) \to -\infty \), and as \( t \to \infty \), \( f(t) \to \infty \). When sketching this function, you’ll begin low on the left, cross the x-axis at the zeros, and rise high on the right. Happy sketching!