Answer:
C. x = -1 ; x ~8.1
Step-by-step explanation:
First we graph [tex]f(x)= -\sqrt{x+2} -3[/tex]
Here we have x+2 under the square root. x+2>=0, x>=-2
So we take some x values greater than -2 and find out f(x) to make a table for graphing
x f(x)
-2 [tex]-\sqrt{-2+2} -3=-3[/tex]
-1 -4
2 -5
Graph it and extent the graph
Now we graph [tex]g(x)= -2|x-3| + 4[/tex]
Given equation is in the form of g(x) = a|x-h| + k
where (h,k) is the vertex
here h= 3 and k = 4, so vertex is (3,4)
Now make a table, pick some numbers for x less than and greater than vertex
x y
-1 [tex]-2|-1-3| + 4=-4[/tex]
0 [tex]-2|0-3| + 4=-2[/tex]
3 4
6 -2
Both graphs are attached below
The graph of f(x) and g(x) interests at x= -1 and x=8.1
