The function provided in the image is:

$f(x) = \frac{3}{2}x - 4$

This is a linear function, where:

• The slope (or rate of change) is $\frac{3}{2}$.
• The y-intercept is $-4$, which is the point where the graph of the function intersects the y-axis.

To analyze this function further:

1. Domain: The domain of $f(x)$ is all real numbers, as there are no restrictions on $x$.
2. Range: Since this is a linear function, the range is also all real numbers.
3. Graph: The graph of this function would be a straight line with a positive slope, rising from left to right, and intersecting the y-axis at $-4$.

Would you like further details, or do you have any questions?

Here are five related questions you might consider:

1. How would you find the x-intercept of $f(x) = \frac{3}{2}x - 4$?
2. What is the effect of changing the slope on the graph of this function?
3. How does the y-intercept affect the position of the graph?
4. How would you find the inverse of $f(x) = \frac{3}{2}x - 4$?
5. How can you determine if this function is increasing or decreasing?

Tip: The slope of a linear function determines the steepness and direction of the line; a positive slope means the line goes up as you move right, while a negative slope means it goes down.