the graph of which of the following rational functions has a hole?
a. y= 2x-6/x-6
b. y= 2x-3/x-3
c. y= 2x-6/ 2x
d. y= 2x-6/x-3
The rational function that has a hole is option d. y= 2x-6/x-3.
To determine if a rational function has a hole, we need to check if there is any factor of the denominator that cancels out with a factor of the numerator, resulting in a hole in the graph.
In option d, the numerator is 2x-6 and the denominator is x-3.
If we simplify the rational function, we can factor out a 2 from the numerator:
y = (2(x-3))/(x-3)
Now we can see that (x-3) cancels out in the numerator and denominator, resulting in a hole at x=3. Therefore, option d has a graph with a hole.