Final answer:
The relation y=1/(x-8) does define y as a function of x, with the domain being all real numbers except 8, and the range being all real numbers. The function can be graphically represented by a hyperbola with vertical and horizontal asymptotes.
Step-by-step explanation:
To determine whether the relation y = 1/(x-8) defines y as a function of x, we need to consider if each value of x corresponds to exactly one value of y. In this case, for every value of x that is not equal to 8, there is exactly one corresponding value of y. This is because the function has a denominator of x-8, which cannot be zero. Therefore, x should not be equal to 8.
The domain of the function is all real numbers except 8, which we can express as x ∈ ℝ, x ≠ 8. The range of the function is all real numbers because for any real value of x (other than 8), you can find a corresponding value of y that makes the equation true.
In general, if the function that describes the dependence of y on x is known, it can be used to compute x,y data pairs that may subsequently be plotted. For this particular function, if we plotted it on a graph, we would get a hyperbola with a vertical asymptote at x=8, reflecting that the function is undefined at this value of x, and a horizontal asymptote at y=0, reflecting that as x increases or decreases without bound, the value of y gets closer to zero. This graphical representation would help visualize the dependence of y on x.