https://file.aiquickdraw.com/mathbot/file/1725837303395zyfxqkkq.jpg

The graph provided appears to represent a curve, possibly a rational function. The curve intersects the point \( (1, -3) \) and exhibits an asymptotic behavior, suggesting that it might be a hyperbola or a rational function.

To find the equation, we can observe the following:

- The curve seems to have a vertical asymptote at \( x = 0 \), meaning the function likely involves a term with \( \frac{1}{x} \).
- The curve also seems to have a horizontal asymptote, likely along the x-axis (though it's not clearly shown).

Let's assume the equation could be of the form:

\[
y = \frac{a}{x} + b
\]

Now, we use the given point \( (1, -3) \) to solve for \( a \) and \( b \).

### Step 1: Plug in \( x = 1 \) and \( y = -3 \) into the assumed equation.

\[
-3 = \frac{a}{1} + b \implies -3 = a + b
\]

This gives us one equation: \( a + b = -3 \).

### Step 2: Use the asymptote information.

- Since there is likely a horizontal asymptote at \( y = 0 \) (as the curve approaches the x-axis), we can assume that \( b = 0 \).

Thus, we now have:

\[
a + 0 = -3 \implies a = -3
\]

### Final Equation:

Substituting \( a = -3 \) and \( b = 0 \) into the general form of the function, we get:

\[
y = \frac{-3}{x}
\]

This is the equation of the curve that matches the observed features: a hyperbolic curve with a vertical asymptote at \( x = 0 \), and it passes through the point \( (1, -3) \).

Would you like more details or have any questions?

### Related questions:
1. How can I find asymptotes of a rational function from its equation?
2. What are the different types of asymptotes a function can have?
3. How can I verify if a point lies on a graph of a function?
4. Can I determine the domain and range of the function \( y = \frac{-3}{x} \)?
5. How do vertical and horizontal shifts affect the equation of rational functions?

### Tip:
Always check the behavior of the function at \( x = 0 \) and \( x \to \infty \) to identify vertical and horizontal asymptotes.

Find the equation of the curve shown in the graph, which passes through the point (1, -3).

Determine the equation of a rational function that passes through the point (1, -3) and exhibits vertical and horizontal asymptotes. Learn how to identify asymptotic behavior and solve for constants using given points.

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