The given function is
f(x) = (x^2 - 9x + 20)/(x - 4)
We would simplify the quadratic function in the denominator. We would find two terms such that their sum or difference is - 9x and their product is 20x^2. The terms are - 5x and - 4x. Thus, we have
x^2 - 5x - 4x + 20
By factorising, we have
x(x - 5) - 4(x - 5)
The function would be
f(x) = (x - 4)(x - 5)/x - 4)
f(x) = x - 5
This is same as
y = x - 5
We would look at the points in each graph, substitute their x and y values and choose the graph that satisfies the function
For the first graph,
if x = - 4 and y = 1, then we have
1 = - 4 - 5 = = 9
This does not satisfy the funtion
For the second graph,
x = 4, y = - 1
- 1 - 4 - 5 = - 1
It satisfies the function
The second graph is correct
For the third graph
x = - 4, y = 9
9 = - 4 - 5 = - 9
This does not satisfy the funtion
For the fourth graph
x = 4, y = - 9
- 9 = 4 - 5 = - 1
This does not satisfy the funtion