Let
Find the Vertical asymptote and write AS A FRACTION.

To find the vertical asymptote of the function , we need to determine where the denominator equals zero, as vertical asymptotes occur at these points. Setting the denominator equal to zero gives us the equation:

Solving for , we add 7 to both sides:

Now, divide both sides by 2:

Thus, the vertical asymptote is located at (which is the fraction format you requested).

Vertical asymptotes indicate where the function approaches infinity or negative infinity, making them key points in understanding the behavior of rational functions. Fun fact: The vertical asymptote occurs whenever the denominator reaches zero without the numerator also being zero at that exact point—as is the case here!

Another thing to remember is to check the limits of the function as it approaches the asymptote from both sides; you’ll see it tends towards positive or negative infinity. This can create interesting behaviors in graphing the function.