Use the leading coefficient test to determine the end behavior of the graph of the given polynomial function \( f(x)=4 x^{7}-2 x^{5}+6 x^{4}+5 \) 112 points \( 42.9 \%, 48.05 \) of A. Rises left \& falls night \( 41,2.3 .19 \) Points: 0 of 2 B. Rises left \& rises night C. Falls left \& falls night D. Falls left \& nises right. E. None of the above

To determine the end behavior of the polynomial function \( f(x) = 4x^7 - 2x^5 + 6x^4 + 5 \), we look at the leading term, which is \( 4x^7 \). Since the leading coefficient (4) is positive and the degree (7) is odd, we can conclude that as \( x \) approaches negative infinity, \( f(x) \) will approach negative infinity (falls left), and as \( x \) approaches positive infinity, \( f(x) \) will approach positive infinity (rises right). Therefore, the correct answer is: D. Falls left & rises right.