How many vertical asymptotes does the graph of this function have?𝐹(𝑥)=3(𝑥−11)(𝑥+4)F(x)= (x−11)(x+4)3​ A.2B.3C.1D.0SUBMITarrow_backPREVIOUS

To determine the number of vertical asymptotes for the function $F(x) = \frac{3}{(x - 11)(x + 4)}$, we need to identify the values of $x$ that make the denominator equal to zero, as these will indicate the potential locations for vertical asymptotes.

Step 1: Identify the Denominator

The denominator of the function is $(x - 11)(x + 4)$.

Step 2: Set the Denominator to Zero

To find the vertical asymptotes, we solve: $(x - 11)(x + 4) = 0$

Step 3: Solve for $x$

Setting each factor to zero gives:

1. $x - 11 = 0$ → $x = 11$
2. $x + 4 = 0$ → $x = -4$

Step 4: Count the Vertical Asymptotes

Since the function has two values of $x$ that make the denominator zero (11 and -4), there are two vertical asymptotes.

Final Answer

Thus, the number of vertical asymptotes for the graph of the function is A. 2.