Answer: g(x) = 5x^2
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Step-by-step explanation:
We're given that f(x) = x^2
The function g(x) is vertically stretched to be five times taller. We see this with the point (1,5) on the purple graph since its counterpart is at (1,1) on the blue graph.
We look at how the y values changed. So we had gone from y = 1 to y = 5. This jump means "multiply by 5"
If we do this to all the y values on the blue graph, then all the points jump to a height 5 times taller. Something like (2,4) moves to (2,20). Something like (3,9) goes to (3,45). And so on. This is what produces the purple g(x) graph.
You could say that
g(x) = 5*f(x)
g(x) = 5x^2
This works because y = f(x), so when we say 5*f(x), we really mean 5*y.