Question

The function f(x)is graphed above. Which of the graphs below represents the function g(x)=(x+1)^2

Answer 1

The function g(x) = (x + 1)² is represented by the graph Y

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;

`\frac{\mathrm{d} (x + 1)^(2)}{\mathrm{d} x} = 2x +2 = 0`

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.