Final answer:
The question involves a rational function with defined vertical and horizontal asymptotes, a hole, and a zero, representing its behavior at certain points in its domain and range.
Step-by-step explanation:
The student's question pertains to the characteristics of a rational function in terms of its asymptotes, holes, and zeros. A vertical asymptote at x=7 indicates that the function approaches infinity or negative infinity as x approaches 7.
Meanwhile, a horizontal asymptote at y=3/2 signifies that as x goes to infinity or negative infinity, the function approaches the value of 3/2. A 'hole' when x=-5 suggests that the function is not defined at this particular x-value due to a common factor in the numerator and denominator of the rational function.
Lastly, a 'zero' at x=1 implies that the function's value is zero when x equals 1. Considering this information, we can surmise that the function resembles a rational function with specific restrictions on its domain and range.