Graphs can be translated horizontally and vertically.

To translate the graph *horizontally*, add or subtract a value *before* the function is applied. The movement is in the *opposite* direction to the value of the addition or subtraction. If `y = f(x)` then `f(x + a)` will cause the graph to be translated by `((-a),(0))`.

To translate a graph *vertically*, add or subtract a value *after* the function is applied. That is, if `y=f(x)` then `y=f(x)+a` will result in a translation of `((0),(a))`.

Sketch the graph of `f(x)=x^2`. Then sketch the graph of `f(x+4)`.

Describe the translation.

To translate a function horizontally, apply the add/subtract *before* evaluating the function.

Answer: The line has been translated `((-4),(0))`

Sketch the graph of `f(x)=x^2`. Then sketch the graph of `f(x)+4`.

Describe the transformation.

To translate a function vertically, apply the add/subtract *after* evaluating the function.

Answer: The line has been translated `((0),(4))`

See also Expressions as Functions and Translation

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