Question

Describe the end behavior of the polynomial f(x) = x⁴ + 2x² – 3x² + x – 10

(a) As x → -[infinity], y →
(b) As x → +[infinity], y =

Answer 1

The end behavior of the polynomial \(f(x) = x^4 + 2x^2 - 3x^2 + x - 10\) is determined by the leading term, which is \(x^4\).

(a) As \(x \to -\infty\), the leading term \(x^4\) dominates, and the polynomial approaches negative infinity. So, \(y \to -\infty\).

(b) As \(x \to +\infty\), the leading term \(x^4\) also dominates, and the polynomial approaches positive infinity. So, \(y \to +\infty\).

Answer 2

The end behavior of the polynomial f(x) = x^4 - x^2 + x - 10 is that as x approaches both negative and positive infinity, y approaches positive infinity.

Step-by-step explanation:

To describe the end behavior of the polynomial f(x) = x⁴ + 2x² − 3x² + x − 10, we first need to simplify the expression by combining like terms. The simplified polynomial is f(x) = x⁴ − x² + x − 10. The end behavior of a polynomial is determined by its leading term, which is the term with the highest power of x. In this case, the leading term is x⁴. For x⁴, as x approaches negative or positive infinity, y will also approach positive infinity, because the leading coefficient (which is 1) is positive and the leading exponent is even.

So, for the end behavior of the function:

• (a) As x → ∞, y → ∞
• (b) As x → +∞, y → ∞

This indicates that the graph will rise to infinity on both ends.