What are the coordinates of the hole in the graph of the function f(x) ?
f(x)=x^2−9/x−3
f(x) = [(x + 3)(x - 3)] / (x - 3)
when x = 3, there is a zero in both the numerator and denominator (hole)
find f(3) to get the coordinates
To find the coordinates of the hole in the graph of the function f(x), you need to determine the value of x for which the expression under the function becomes undefined. In this case, the expression becomes undefined when the denominator (x - 3) equals zero. Setting the denominator equal to zero and solving for x, we get:
x - 3 = 0
Adding 3 to both sides:
x = 3
Now that we have the value of x, we can find the corresponding y-value by plugging it back into the original function f(x):
f(3) = (3^2 - 9) / (3 - 3)
= (9 - 9) / 0
= 0 / 0
Notice that we have a zero in both the numerator and the denominator. This indicates an indeterminate form, which means the expression does not have a specific value and the function has a hole at this point.
Therefore, the coordinates of the hole in the graph are (3, 0).