Question

The function f(x) is defined below. What is the end behavior of f(x) ? f(x)=7x⁴+35x³-280-231x²-539x

Answer 1

The end behavior of the function f(x) = 7x⁴ + 35x³ - 280 - 231x² - 539x is that as x approaches either positive or negative infinity, f(x) approaches positive infinity.

Step-by-step explanation:

The question relates to determining the end behavior of a polynomial function given by f(x) = 7x⁴ + 35x³ - 280 - 231x² - 539x. Because the highest power of the variable x in the function determines the end behavior, we need only look at the term 7x⁴.

As x approaches positive or negative infinity, the end behavior of the function will resemble that of y = 7x⁴, which means that f(x) will approach positive infinity as x approaches positive infinity and that f(x) will approach positive infinity as x approaches negative infinity, since the leading term has an even exponent and a positive coefficient.

Thus, the end behavior of the function f(x) is such that:

• As x approaches positive infinity (∞), f(x) approaches positive infinity.
• As x approaches negative infinity (-∞), f(x) also approaches positive infinity.