Hello!
This equation is looking at domains and equations.
The domain of an equation is its x value. For example, a domain of 0 < x < 1 would be the area of the function with an x value between 0 and 1.
Function equations define the equation of a line. f(x), in this case, also means y.
Now, looking at the piecewise function, we can find the equation for each domain. (Side note: the only real difference between the < ≤ and > ≥ in this scenario is just if the dot is colored in or not, in this case. It does matter normally, just not for this question)
3 < x ≤ 4: Look at the section where the x value is between 3 and 4. The line has a y value of 4. This means the equation would be f(x) = 4, or, y = 4.
1 ≤ x ≤ 2: This one's slightly more complicated, as the line is not just horizontal or vertical. Look at an equation of a line, y = mx + b, where m is the slope and b is the y intercept. In this case, the slope is just 1, as for every one x unit, the line moves up one y unit. The y intercept is just 0, as there is a point (1, 1), and as the slope is 1, there will be a point of (0, 0). Therefore, the equation for this would be y = 1x + 0, or just f(x) = x.
2 < x ≤ 3: Another straight line in this case, and the y value is 3, so f(x) = 3
0 < x ≤ 1: Straight line, y value is equal to 1, so f(x) = 1
Hope this helped!
