This means x = -1 and y = 11 pair up together.
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Work Shown:
Set the two functions equal to one another. Solve for x.
f(x) = g(x)
-4x+7 = 2x+13
7 = 2x+13+4x ... adding 4x to both sides
7 = 6x+13
7-13 = 6x .... subtract 13 from both sides
-6 = 6x
6x = -6
x = -6/6 ... divide both sides by 6
x = -1
Use this x value in either function
f(x) = -4x+7
f(-1) = -4(-1)+7
f(-1) = 11
or
g(x) = 2x+13
g(-1) = 2(-1)+13
g(-1) = 11
Whichever function you pick, the input x = -1 leads to the output y = 11.
The point of intersection is (x,y) = (-1, 11)
Visual confirmation is shown below.
ANSWER
The domain of the function is
or
[-3,6]
EXPLANATION
The domain of a function refers to the values of x for which the function is defined.
From the graph, we can see that the function begins at (-3,6) and ends at (6,-4).
Therefore the function is defined for x=-3 to x=6.
Hence the domain of the function is
or
[-3,6]