Answer:
- See the attachment for the graph
- Reflection across the line y = 1/2 will change f(x) to g(x)
Step-by-step explanation:
The two functions have opposite slope, so reflection across a horizontal line will change one to the other. The line of reflection will be the horizontal line through the point of intersection of these functions. The y-value of that point is halfway between the y-intercepts -2 and +3, so is 1/2.
The transformation can be described by ...
... g(x) = -(f(x) -1/2)) +1/2 . . . . reflection across the line y = 1/2
... g(x) = -f(x) +1 . . . . . . . . . . . simplified
Check
... g(x) = -(-x-2) +1 = x+2+1 = x+3 . . . . yes
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Alternate solution
The functions could also be a reflection of each other across the vertical line through their point of intersection at x=-5/2.
... g(x) = f(-(x +5/2) -5/2)
... g(x) = f(-x-5) . . . . . . . . . . simplified
Check
... g(x) = -(-x-5) -2 = x+5-2 = x+3 . . . . yes
