Answer:
The function g(x) = (x + 1)² is represented by the graph Y
Step-by-step explanation:
The question presents the graph of the function x² above
Therefore, for a function f(x) = x² at x = 0 y = 0
For function g(x) = (x + 1)² when x = 0 g(x) = 1 Satisfied by graph W and Y
Also we have g(x) = (x + 1)² = x² + 2·x + 1 or g(x) = f(x) + 2·x + 1
We find the minimum of the graph by differentiating and equating to zero as follows;
[tex]\frac{\mathrm{d} (x + 1)^{2}}{\mathrm{d} x} = 2x +2 = 0[/tex]
Therefor, the minimum is at x = -1 satisfied by only graph Y
Hence the graph that represents the function g(x) = (x + 1)² is the graph Y.
