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Describing Transformations of Linear Functions

a

A horizontal translation is a shift of a graph along the -axis. This means we have to manipulate the inputs of the original function. To move a function by units to the left, we have to add to the function's inputs. We get: We want the graph of to be a horizontal translation units to the left of the graph of This means we have to add to

b

A reflection is a transformation that flips a graph over a line called the line of reflection. A reflection in the -axis, means that the -values stay the same, but the signs of the -values are changed. To change the sign of the outputs from the function we have to multiply the function by