Question

Can you give an example of a function for which a horizontal translation gives the same resulting graph as a vertical translation? Explain.

Answer 1

Answer:

Any linear function, like f(x) = 3x +2

Step-by-step explanation:

Translating this function to the right 1 unit gives ...

... f(x -1) = 3(x -1) +2 = 3x -1

Translating this function down 3 units gives ...

... f(x) -3 = (3x +2) -3 = 3x -1

You will note that the chosen horizontal translation produces the same result as the chosen vertical translation.

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The corresponding translations are related to the slope of the graph. For a linear function, the slope is the same everywhere, so the necessary vertical and horizontal translations that map the function to itself are the same everywhere.