Question

Determine the end behavior of P(x⁴ - 8x² + 7x + 3).

a) As x approaches infinity, P(x) approaches [infinity]; as x approaches -[infinity], P(x) approaches -[infinity]
b) As x approaches infinity, P(x) approaches -[infinity]; as x approaches -[infinity], P(x) approaches [infinity]
c) As x approaches infinity, P(x) approaches [infinity]; as x approaches -[infinity], P(x) approaches [infinity]
d) As x approaches infinity, P(x) approaches -[infinity]; as x approaches -[infinity], P(x) approaches -[infinity]

Answer 1

The end behavior of the polynomial function can be determined by examining the leading term, which is x⁴. In this case, as x approaches infinity or negative infinity, P(x) approaches positive infinity.

Step-by-step explanation:

The end behavior of a polynomial function can be determined by examining the leading term, which is the term with the highest degree. In this case, the leading term is x⁴. When the degree of the leading term is even and the leading coefficient is positive, the end behavior of the function is as follows:

• As x approaches infinity, P(x) approaches positive infinity.
• As x approaches negative infinity, P(x) also approaches positive infinity.

Therefore, the correct answer is option c) As x approaches infinity, P(x) approaches [infinity]; as x approaches -[infinity], P(x) approaches [infinity].