From the images provided, I can see that you are working on identifying the vertical and horizontal asymptotes of a function based on its graph.

Vertical Asymptotes:

Vertical asymptotes occur where the function approaches infinity as $x$ approaches a certain value. In the graph, this is visible at sharp upward or downward spikes. Observing the graph:

• The function seems to approach infinity near $x = 1$, suggesting a vertical asymptote at $x = 1$.

Horizontal Asymptotes:

Horizontal asymptotes represent the value the function approaches as $x$ goes to infinity or negative infinity. Looking at the graph:

• As $x$ goes to positive infinity, the function appears to flatten out near $y = 0$, indicating a horizontal asymptote at $y = 0$.

Summary of Asymptotes:

• Vertical asymptote: $x = 1$
• Horizontal asymptote: $y = 0$

Would you like more details or further clarifications?

Here are 5 related questions to expand your understanding:

1. How do you identify vertical asymptotes for rational functions from their equations?
2. Can a function have more than one horizontal asymptote?
3. What is the difference between horizontal and slant asymptotes?
4. How do you determine the asymptotes of a logarithmic or exponential function?
5. What happens at an asymptote when a function "crosses" it?

Tip:

For rational functions, vertical asymptotes occur where the denominator equals zero, and horizontal asymptotes depend on the degree of the numerator relative to the denominator.