The graph you provided appears to show a function that exhibits asymptotic behavior along the y-axis and a rapid increase for both positive and negative values of $x$. This type of behavior is characteristic of a logarithmic or reciprocal function.

Given the steep rise on both sides of the graph and its vertical asymptote at $x = 0$, this graph likely represents a reciprocal function, of the form:

$f(x) = \frac{1}{x}$

Here's why:

1. Vertical Asymptote: There is a vertical asymptote along the y-axis, which corresponds to $x = 0$, where the function is undefined.
2. Behavior for Positive and Negative $x$: For $x > 0$, the function increases steeply, and for $x < 0$, it decreases steeply in the opposite direction, which is typical of reciprocal functions.

Would you like more detailed analysis or to confirm this? Here are five questions to deepen your understanding:

1. How does the vertical asymptote of a function relate to its domain?
2. What are the horizontal asymptotes of the function $f(x) = \frac{1}{x}$?
3. How can you identify asymptotic behavior in a graph?
4. What transformations could be applied to the basic function $f(x) = \frac{1}{x}$ to shift or stretch it?
5. How does the function behave as $x$ approaches $0$ from both sides?

Tip: Reciprocal functions have undefined values at their vertical asymptotes—make sure to check the domain carefully!