Describe the end behavior of each polynomial.

Question

(a)    y = x³ − 8x² + 9x − 15

End behavior:

y---> ______ as x → ∞

y---> ______ as x → -∞

(b)    y = −9x⁴ + 14x + 400

End behavior:

y---> ______ as x → ∞

y---> ______ as x → -∞

Answer 1

a) When x is very large and positive, y = x³ − 8x² + 9x − 15 is dominated by x³. Hence, y -> ∞ as x -> ∞.

When x is very large and negative, y = x³ − 8x² + 9x − 15 is dominated by x³. Hence, y -> -∞ as x -> -∞.

b) When x is very large and positive, y = −9x⁴ + 14x + 400 is dominated by -9x³. Hence, y -> -∞ as x -> ∞.

When x is very large and negative, y = −9x⁴ + 14x + 400 is dominated by -9x³. Hence, y -> ∞ as x -> -∞.