Let's analyze the linear function $f(x) = \frac{2}{3}x + 4$ and answer the questions from the image.

a) Integer coordinates of the y-intercept

The y-intercept occurs when $x = 0$. Substituting $x = 0$ into the equation:

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

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

b) Integer coordinates of the x-intercept

The x-intercept occurs when $f(x) = 0$. Set the function equal to 0 and solve for $x$:

$0 = \frac{2}{3}x + 4$ $\frac{2}{3}x = -4$ $x = -4 \times \frac{3}{2} = -6$

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

c) Domain of the function

The function is a linear function, which means it is defined for all real values of $x$. Therefore, the domain is:

$(-\infty, \infty)$

d) Range of the function

Since the function is linear and its graph is a straight line that extends infinitely in both directions, the range is also all real values:

$(-\infty, \infty)$

e) Is the function increasing or decreasing?

The slope of the function is $\frac{2}{3}$, which is positive. This means the function is increasing on its domain.

Would you like any further details or explanations? Here are five related questions you might want to explore:

1. How do you graph linear functions on DESMOS?
2. What is the effect of the slope on the steepness of a linear graph?
3. How do you find the slope of a line given two points?
4. How do domain and range differ for different types of functions?
5. How does the behavior of a function change if the slope is negative?

Tip: Always check the sign of the slope to determine if a function is increasing or decreasing. A positive slope means the function increases, while a negative slope means it decreases.