Question

Describe the end behavior of the graph of the polynomial function by completing these statements: f(x)→? as x→-∞ and f(x)→? as x→+∞.

1. f(x)=-(x^2)+1
2. f(x)==10x^3

Answer 1

(1) f(x)=-(x²)+1
is a parabola concave downwards, with a y-intercept of 1.
Thus the behaviour toward both infinities are -∞.

2. f(x)=-10x³ (note correction of typo)
is a cubic polynomial that starts from +∞ when x->-∞, and finishes off at -∞ as x->∞.