Apparently this thing goes from green to violet to blue1 to blu2. there is a break at (0, - 3)
All I can do is show answers for the colors. You are going to have to figure out what the choices are and where to put them.
Green
Slope = (y2 - y1)/(x2 - x1)
y2 = -7
y1 = -4
x2 = 7
x1 = 4
m = (-7 - - 4) / (7 - 4)
m = - 3 / 3 = -1
So far what we have is
y = -x + b
Use one of the points to solve for b
(4,-4) This means that when x = 4, y = -4
-4 = -4 + b
b = 0
The answer to green is that
4 <x < 7
-7 < f(x) < - 4
Wine or Red color
This is actually a exponential equation or part of. The general formula for it is
y = 2 ^ x but there are restrictions.
1 < x < 4
2 < y < 16 Notice that the end points are not included (empty circles).
Blue 1
The x value goes from 0 to 1 and it is inclusive.
The y value goes from -3 to - 2 and that is inclusive as well.
Equation
m = (y2 - y1) / (x2 - x1)
m = (1 - - 2) / (0 - - 3)
m = 3 /3 = 1
So the equation for the line
f(x) = x + b. Use one of the points to solve for b
-3 = 0 + b
b = - 3
f(x) = x - 3 is the equation of blue1.
Blue2
the x value goes from 0,-3 to infinity.
From the graph, the x intercept is (-3, 0)
y = mx + b
-3 = 0 + b
b = -3
So far we have
y = mx - 3
0 = -3m - 3
3 = - 3m
m = -1
So this equation is y = -x - 3
so
- infinity < x <= 0
- inifinity < x <= - 3
That's as far as I can go because I really don't know what the drop downs say. You are stuck having to take the information I've found and work with it.