Let's go step by step to address the problem in the image:

1. Vertical Line Test:

The vertical line test is used to determine whether a curve on a graph represents a function. According to this test, if any vertical line intersects the graph more than once, then the graph does not represent a function.

In this case, the provided graph passes the vertical line test because any vertical line would intersect the curve at only one point. Thus, $y$ is a function of $x$.

The correct answer to this part is:

• Yes, $y$ is a function of $x$.

2. Solving for $y$:

The equation given is: $x^2 = 3xy - 4$ We need to solve this equation for $y$.

1. Start by isolating the $y$ term: $x^2 + 4 = 3xy$

2. Solve for $y$: $y = \frac{x^2 + 4}{3x}$

Thus, the equation of the graph is: $y = \frac{x^2 + 4}{3x}$

This function can be input into a graphing utility to produce the provided graph.

Do you have any questions or would you like further clarification?

5 Related Questions:

1. How do you use the vertical line test for more complex graphs?
2. Can a function have more than one $y$-value for a given $x$-value?
3. What happens when the denominator of a function becomes zero?
4. How can transformations of functions be visualized on a graph?
5. How would you find the asymptotes of the function $y = \frac{x^2 + 4}{3x}$?

Tip:

When solving equations involving $y$, always check for cases where the function might be undefined, such as division by zero!