The function $f(x)$ in the image shows a vertical asymptote near $x = -2$. This indicates that the function might be in the form of a rational expression like:

$f(x) = \frac{a}{x + b} + c$

where:

• $b$ would shift the vertical asymptote to $x = -2$,
• $a$ affects the "steepness" or "stretch" of the curve, and
• $c$ would indicate any horizontal shift.

For vertical asymptotes:

1. If the function has a vertical asymptote at $x = -2$, then we set $b = 2$ so that the denominator becomes zero when $x = -2$.

2. The general form could then be: $f(x) = \frac{a}{x + 2} + c$

Would you like to go further into finding the exact values for $a$ and $c$ based on other points on the curve?

Here are 5 related questions for further exploration:

1. What is a vertical asymptote, and how is it determined for rational functions?
2. How does the value of $a$ in $\frac{a}{x + b}$ impact the graph's shape?
3. What role does the constant $c$ play in shifting the graph vertically?
4. How can you use other points on the graph to find specific values of $a$ and $c$?
5. How does the horizontal asymptote differ from the vertical asymptote in rational functions?

Tip: To find the vertical asymptote, identify the $x$-value where the function approaches infinity or negative infinity.