Determine the end behavior of the function \(f(x) = -3x^4 + 2x^2 - 1\) using the Leading Coefficient Test
Answer
For a polynomial function with an even degree and a negative leading coefficient, as \(x\) approaches positive infinity, \(f(x)\) approaches negative infinity, and as \(x\) approaches negative infinity, \(f(x)\) also approaches negative infinity.
Step 1 ：The leading coefficient test states that the end behavior of a polynomial function is determined by its degree and the sign of the leading coefficient.
Step 2 ：In the function \(f(x) = -3x^4 + 2x^2 - 1\), the degree is 4 (even) and the leading coefficient is -3 (negative).
Step 3 ：For a polynomial function with an even degree and a negative leading coefficient, as \(x\) approaches positive infinity, \(f(x)\) approaches negative infinity, and as \(x\) approaches negative infinity, \(f(x)\) also approaches negative infinity.
