at which values of x does the graph of (f(x)=\frac{x^{2}-x - 2}{(x^{2}-1)(x^{2}-16)}) have a vertical…

at which values of x does the graph of (f(x)=\frac{x^{2}-x - 2}{(x^{2}-1)(x^{2}-16)}) have a vertical asymptote? check all that apply.\n-4\n-1\n1\n2\n4

at which values of x does the graph of (f(x)=\frac{x^{2}-x - 2}{(x^{2}-1)(x^{2}-16)}) have a vertical asymptote? check all that apply.\n-4\n-1\n1\n2\n4

Answer

Explanation:

Step1: Find when the denominator is zero

Set ((x^{2}-1)(x^{2}-16)=0). Since (a^{2}-b^{2}=(a + b)(a - b)), we have ((x + 1)(x - 1)(x+4)(x - 4)=0).

Step2: Solve for x

Using the zero - product property, if (ab = 0), then (a = 0) or (b = 0). (x+1=0) gives (x=-1); (x - 1=0) gives (x = 1); (x + 4=0) gives (x=-4); (x - 4=0) gives (x = 4).

Answer:

-4, -1, 1, 4