Final answer:
The function y = (x+4)/(x²+5x+4) has a hole at x = -4, which is found by factoring the denominator and identifying the common term with the numerator.
Step-by-step explanation:
The student is asking whether a hole exists in the function y = (x+4)/(x²+5x+4). To determine this, we first need to factor the denominator to see if there are any values of x that will make the denominator zero, which would indicate the presence of a hole or an asymptote when there is a common factor in the numerator and denominator.
The denominator factors as (x+4)(x+1). Since the numerator is also (x+4), we can simplify the function to y = 1/(x+1) after canceling out the (x+4) term. This cancellation indicates that there is indeed a hole at x = -4, because the value x = -4 causes the denominator to be zero before the simplification, but does not exist in the simplified function.