To determine the vertical asymptotes and holes of the function y = x^3 + 1x + 1x + 5, we first need to look at the function closely.
First, let’s simplify the function. The standard form is:
y = x^3 + 2x + 5
Next, to find vertical asymptotes, we need to identify values of x that make the denominator zero (if this were a rational function) and lead to undefined behavior. However, this function is not a fraction, so there are no vertical asymptotes present.
Now, we need to check for holes in the graph. Holes occur in rational functions when we have a factor in the numerator that cancels out with a factor in the denominator. Since our expression is a polynomial and does not have a denominator, there are no holes in this function either.
To summarize, for the function y = x^3 + 2x + 5, there are no vertical asymptotes or holes. The graph is continuous everywhere as it is a polynomial function.