Presentation on theme: "Parent Functions and Transformations. Transformation of Functions Recognize graphs of common functions Use shifts to graph functions Use reflections to."— Presentation transcript:
We will now see how certain transformations (operations) of a function change its graph. This will give us a better idea of how to quickly sketch the graph of certain functions. The transformations are (1) translations, (2) reflections, and (3) stretching.
Vertical Translation OUTSIDE IS TRUE! Vertical Translation the graph of y = f(x) + d is the graph of y = f(x) shifted up d units; the graph of y = f(x) d is the graph of y = f(x) shifted down d units.
Horizontal Translation INSIDE LIES! Horizontal Translation the graph of y = f(x c) is the graph of y = f(x) shifted right c units; the graph of y = f(x + c) is the graph of y = f(x) shifted left c units.
The values that translate the graph of a function will occur as a number added or subtracted either inside or outside a function. Numbers added or subtracted inside translate left or right, while numbers added or subtracted outside translate up or down.
Recognizing the shift from the equation, examples of shifting the function f(x) = Vertical shift of 3 units up Horizontal shift of 3 units left (HINT: x’s go the opposite direction that you might believe.)