How do you graph a function using a translation?

Question

Graph a function using a translation. Provide an step by step example and graphed solution.

Answer 1

Example: The graph of f(x) = x² is a parabola opening upward with lowest point (0,0).

Graph of f(x-2) = (x-2)² can be obtained by translating the graph of y = f(x) two units to the right.

Graph of f(x) - 2 = x² - 2 can be obtained by translating the graph of y = f(x) two units downward.

Answer 2

That depends entirely on the given function and the required translations. You did not provide either.

Answer 3

Compared to graph of a function f(x), the graph of f(x − a) + b will be translated horizontally by a units and vertically by b units. (Positive translation is to the right horizontally and up vertically.)

For example, if you compare the graph of f(x) = x² to that of g(x) = f(x − 2) + 4 = (x − 2)² + 4:

The graph of f(x) will be a parabola with its vertex at origin. The graph of g(x) will be a translated parabola (identical to the first parabola except for its position) shifted to the right by 2 units and up by 4 units. The vertex of g(x) will be shifted to the point (2,4).