Describe the vertical asymptotes and holes for the graph of y = x - 4/x² + 3x + 2

Solution:

The given equation is:

y = (x - 4)/(x² + 3x + 2)

y = (x - 4)/(x² + 2x + x + 2)

y = (x - 4)/[x(x + 2) + 1.(x + 2)

y = (x - 4)/(x + 1)(x + 2)

When x = -1 and when x = -2 the function y → ∞

Hence the vertical asymptotes of the given function are:

x = -1

And

x = -2

Since there are no common factors in the expression y = (x - 4)/(x + 1)(x + 2) there are no holes for the graph of the given function y.

Describe the vertical asymptotes and holes for the graph of y = x - 4/x² + 3x + 2

Summary:

The vertical asymptotes of the given function’s graph are x = -1 and x = -2.