(11 points) 3. \( f(x)=x^{3}-3 x^{2}-5 x^{4}+7 \) Identify the... Degree \( \qquad \) Leading Coefficient \( \qquad \) Constant Term \( \qquad \) End Behavior: (9 points) \( \qquad \) \( \qquad \) \( \qquad \) \( \qquad \) \( \qquad \) \( \qquad \) \( \qquad \) \( \qquad \) \( \qquad \) \( \qquad \) (1 point each) (11 points) 4. \( f(x)=-2-5 x^{7}+4 x^{8}-4 x^{6} \) Identify the... Degree \( \qquad \) Leading Coefficient \( \qquad \) Constant Term \( \qquad \) End Behavior: (9 points) A. \( 4 x^{4}-2 x^{2}+6 \) B. \( -x^{3}+16 x^{2}+2 x+16 \) C. \( 3 x^{2}+12 x+7 \) D. \( -5 x+8 \) E. \( 7 x^{3}-2 \) F. \( 14 x^{2} \) G. \( 5 x^{4}+4 x^{3}-8 x^{2}+5 x \) H. 8 I. \( 8 x^{3}-10 x+7 \) J. \( -x^{4} \)

For the first function \( f(x) = x^{3} - 3x^{2} - 5x^{4} + 7 \): - The degree is the highest power of \( x \) in the polynomial, which is 4. - The leading coefficient is the coefficient of the highest degree term, which is -5. - The constant term is the term without \( x \), which is 7. End Behavior: As \( x \to -\infty \), \( f(x) \to -\infty \) (because the leading term dominates). As \( x \to \infty \), \( f(x) \to -\infty \) as well. For the second function \( f(x) = -2 - 5x^{7} + 4x^{8} - 4x^{6} \): - The degree is 8, as the highest power is \( x^{8} \). - The leading coefficient is 4, associated with the \( x^{8} \) term. - The constant term is -2. End Behavior: As \( x \to -\infty \), \( f(x) \to -\infty \) because the leading term has a positive coefficient and is dominant, and as \( x \to \infty \), \( f(x) \to \infty \). Here we find ourselves deep in the numeric world of polynomials! Understanding these can help you navigate the various behaviors of equations and their graphs—like predicting the weather but for math! When it comes to grappling with polynomial functions, plotting them can be your greatest ally! Grab some graph paper or a digital plotting tool, and watch those equations come to life. This hands-on experience can illuminate patterns that mere calculations might obscure! Plus, it's a fun way to spend a weekend or impress your friends with your newfound math wizardry.