Given the polynomial function \(f(x) = -2x^5 + 3x^4 - 7x^3 + 2x^2 - x + 1\), describe the end behavior of the function using the Leading Coefficient Test.
Answer
Step 2: Because the degree is odd and the leading coefficient is negative, the end behavior of the function is: as \(x \to -\infty, f(x) \to +\infty\) and as \(x \to +\infty, f(x) \to -\infty\). This is according to the Leading Coefficient Test.
Step 1 ：Step 1: Identify the degree and leading coefficient of the polynomial. The degree is 5 (the highest exponent of x) and the leading coefficient is -2.
Step 2 ：Step 2: Because the degree is odd and the leading coefficient is negative, the end behavior of the function is: as \(x \to -\infty, f(x) \to +\infty\) and as \(x \to +\infty, f(x) \to -\infty\). This is according to the Leading Coefficient Test.
