x − 3 − 2 − 1 0 1 2 3
y = 2 x 1 8 1 4 1 2 1 2 4 8


notification that the graph has the x -axis as an asymptote top top the left, and increases really fast on the right.

transforming the basic transforms the form of the graph.


instead of x with − x reflects the graph across the y -axis; replacing y through − y reflects it across the x -axis.


replacing x with x + h translates the graph h systems to the left.


instead of y through y − k (which is the exact same as adding k to the right side) equates the graph k devices up.


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