Suppose the the limit as x approaches 6 to the left equals infinity. What conclusion can be made about the graph of y = f (x)?
there is a horizontal asymptote at y = -6
there is a horizontal asymptote at y = 6
there is a vertical asymptote at x = -6
there is a vertical asymptote at x = 6
we know x is not going to infinity, so the asymptote must be vertical.
(D)
To determine the conclusion about the graph of y = f(x) when the limit as x approaches 6 from the left equals infinity, we need to understand the concept of limits and their relationship to asymptotes.
An asymptote is a line that a curve approaches, but never touches or crosses. There are two types of asymptotes: horizontal and vertical.
A horizontal asymptote is a horizontal line that the curve approaches as x goes towards positive or negative infinity.
A vertical asymptote is a vertical line that the curve approaches, but does not touch, as x approaches a specific value.
In this case, since the limit as x approaches 6 from the left equals infinity, we can conclude that there is a vertical asymptote at x = 6. This means that the curve of the graph y = f(x) approaches the vertical line x = 6 as x gets closer to 6, but never touches or crosses it.
Therefore, the correct conclusion is: "There is a vertical asymptote at x = 6."