Question

G is a transformation of f. The graph below shows f as a solid blue line and g as a dotted red line. What is the formula of g in terms of f?

Answer 1

Answer: f(x-2) which is choice A.

The blue f(x) curve is shifted 2 units to the right to get the red g(x) dashed curve.

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Explanation:

For now, ignore the red dashed curve g(x). Imagine that the blue curve f(x) is fixed in place. If we shifted the xy axis to the left 2 units, then this gives the illusion the blue curve is moving even though the curve is fixed in place.

The operation "shift xy axis 2 units to the left" means each x input is 2 units smaller. So each x input is now x-2.

Therefore, going from f(x) to f(x-2) will shift the blue curve 2 units to the right to land perfectly on the red dashed g(x) curve.