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You can use the equation of a function to write an equation for its transformation. For example, let
G of x is equal to negative f times the quantity of x plus three, plus 10. Arrow pointing to negative f with label “reflect across x axis.” Arrow pointing to x plus three with label “shift left 3.” Arrow pointing to plus 10 with label “shift up 10.”
Which means
Sometimes you can recognize from the expression for a function that it is the transformation of a simpler function. For example, consider:
One way to obtain the expression for
So the graph of