Find the Behavior (Leading Coefficient Test) f(x)=-x^2(x+4)(x^2-1)

Problem

ƒ(x)=−x2*(x+4)*(x2−1)

Solution

1. Identify the degree of each factor in the polynomial function.

2. Determine the total degree n by adding the exponents of the variable x in each factor: 2 + 1 + 2 = 5$.

3. Identify the leading coefficient (a_n) by looking at the sign and constant multiplying the highest power of x

4. Observe that the leading coefficient is −1 which is negative ((a_n)<0.

5. Apply the Leading Coefficient Test for an odd degree (n=5 and a negative leading coefficient.

6. Conclude the end behavior: as x→∞ ƒ(x)→−∞ and as x→−∞ ƒ(x)→∞

Final Answer

As *x→∞,ƒ(x)→−∞* and as *x→−∞,ƒ(x)→∞

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