Question

Consider the following Polynomial.

S(x)= -3x^2 +x-9
Describe the behavior of the graph of S(x) as x ---> +/- ∞

S(x)--> ? as x--> -∞
S(x)-->? as x-->∞

Answer 1

• S(x) → -∞ as x → -∞
• S(x) → -∞ as x → ∞

Explanation:

The leading term tells you what you want to know. It is of even degree, so the value of S(x) is the same regardless of the sign of x as the magnitude of x gets large.

The sign of S(x) matches the sign of the leading coefficient (-3), so is negative as x gets large.

Hence ...

• S(x) → -∞ as x → -∞
• S(x) → -∞ as x → ∞