Question

P(x)=4x⁵−8x³−7x²+9x+7,

P(x)→
if x→−[infinity]
P(x)‐
if x→[infinity]
If your answer is −[infinity]−[infinity], input -infinity; if your answer is [infinity][infinity],
input infinity.

Answer 1

Answer:When x→−∞ , then P(x)→−∞When x→+∞ , then P(x)→+∞Note that we can figure out if the function grows or decreases, simply by looking at the leading term of the function which is 4x⁵. This term shows that the function increases without bound as x → ± ∞.The given function is P(x)=4x⁵−8x³−7x²+9x+7We can now find the horizontal asymptotes of the given function, by computing the limits at infinity as follows;When x→−∞ , then P(x)→-∞When x→+∞ , then P(x)→+∞Therefore, the horizontal asymptotes are: y= - ∞ and y= + ∞