Question

This is a sketch of the curve with equation y = f(x).

The curve has a minimum point at M(-1, -3).
Write down the coordinates of the minimum point
of the curve with equation
y = f(x) - 2

Answer 1

(-1, -5)

Explanation:

Each point on a graph is the ordered pair (x, f(x)). Then the point M(-1 -3) is the ordered pair (-1, f(-1)) where f(-1) = -3.

A point on the shifted graph will be ...

(x, f(x) -2)

Then for x = -1, the point is ...

(-1, f(-1) -2) = (-1, -3 -2) = (-1, -5)

The minimum on the shifted curve is M'(-1, -5).

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Additional comment

f(x) is the y-coordinate of a point on a graph. Then f(x) -2 is the y-coordinate shifted down 2 units.