Which function does the graph represent?

f(x) = (x + 3)(x + 7)
f(x) = (x – 3)(x – 7)
f(x) = 3(x – 3)(x – 7)
f(x) = 11(x + 3)(x + 7)

The answer is (c) f(x) = 3(x – 3)(x – 7)

Step-by-step explanation:  We are given a graph of a function f(x) and four options out of which we are to select the correct function that the graph represent.

From the graph, we have

f(3) = 0, f(7) = 0.

So, the options f(x) = (x + 3)(x + 7) and f(x) =11 (x + 3)(x + 7) are not correct.

The remaining choices are f(x) = (x – 3)(x – 7)  and f(x) = 3(x – 3)(x – 7).

From the graph we have f(5) = -12, which is satisfied by the function f(x) = 3(x-3)(x-7), not the other one.

Thus, the correct option is (c) f(x) = 3(x – 3)(x – 7).