I see you've uploaded an image with questions about analyzing a linear function. The function in question is:

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

Let's go through the questions one by one:

a) State the integer coordinates of the y-intercept:

The y-intercept occurs when $x = 0$. To find the y-intercept, substitute $x = 0$ into the equation:

$f(0) = -\frac{2}{3} (0) + 4 = 4$

Thus, the y-intercept is at $(0, 4)$.

b) State the integer coordinates of the x-intercept:

The x-intercept occurs when $y = 0$. Set $f(x) = 0$ and solve for $x$:

$0 = -\frac{2}{3} x + 4$

Rearranging the equation:

$\frac{2}{3} x = 4$

Multiply both sides by $3$:

$2x = 12$

Now, divide by 2:

$x = 6$

Thus, the x-intercept is at $(6, 0)$.

c) State the interval for $x$ representing the mathematical domain:

Since this is a linear function (a straight line), the domain of $x$ is all real numbers. So, the domain is:

$(-\infty, \infty)$

d) State the interval for $y$ representing the mathematical range:

For a linear function, the range is also all real numbers. So, the range is:

$(-\infty, \infty)$

e) Is this function increasing or decreasing on its domain?

The slope of the line is $-\frac{2}{3}$, which is negative. This means the function is decreasing on its domain.

f) Fill in the end-behavior: as $x \to +\infty$, $y \to$ ?

As $x \to +\infty$, since the slope is negative, $y \to -\infty$.

g) Fill in the end-behavior: as $x \to -\infty$, $y \to$ ?

As $x \to -\infty$, since the slope is negative, $y \to +\infty$.

Let me know if you need further explanations or if you'd like to explore related questions! Here are 5 related questions you may find interesting:

1. How do you determine the slope and y-intercept of a linear function from its equation?
2. How would the graph of this linear function look if the slope were positive instead of negative?
3. What would happen to the graph if the constant term in the equation (the y-intercept) changed?
4. How can you identify the increasing or decreasing nature of a linear function by its slope?
5. What is the significance of the domain and range in the context of real-world problems?

Tip: The slope of a linear function tells you the rate at which $y$ changes with respect to $x$, while the y-intercept is where the graph crosses the y-axis.