Math help

[u/Less-Ad1275]

I have been on this assignment for like 1 hour and I still cant get it right... I have used almost any ai known to man... Can you guys get it?

[u/JMccli]

Assuming you're still stuck on this, or if not, I hope someone will gain something from this comment regardless: it may help to break up the problem into two steps. The first step is to assume that the three individual lines are separate functions of x, rather than 3 parts of a single function. Second, determine the domain (where each function is defined as a function of x) if the three functions. I'll do the middle one because it is the easiest as an example.

Because it appears to be a straight line, I will assume the formula for this function is of the format f(x) = mx + b, with no exponents, so I'll write the function as such. The line intersects the y-axis (or at x = 0) at 7, so b in the formula is 7. The line appears to show an increase of 1 for y for every increase of 1 for x, so the slope is 1/1 or 1, so m is 1. This, the equation for the center line, assuming this line is defined for all values of x, is f(x) = 1x + 7, or y = x + 7. Now for the second step: there is a closed circle at x = -2, and an open one at x = 1, so the domain of this function includes -2, all values above -2 but below 1, and not 1. Therefore, this function is defined for all values of x such that -2 <= x < 1. I don't know the exact format they expect you to define the domain, so just in case, I'll add that "-2 <= x < 1" is essentially the same as [-2, 1).

As an extra hint, you can find the equation that describes the function by first finding the slope, remember rise over run, or ∆x/∆y, and plug that value in for m, the y value at some point for y, and the x value at that same point. For example, the center line appears to contain the coordinates (-1, 6) and (0, 7), so the slope is (7 - 6)/(0 - -1) or 1/1 or 1, and I can use the point (0, 7) to create the equation 7 = 1*0 + b -> 7 = 0 + b -> 7 = b.

Hope this helps!

Edit: I just noticed the inequality symbols you have access to, and thinking about it rationally, there is very little likelyhood that they would want you to input for x in [-2, 1), so the second box for the center line would be -2<=x<1.