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## Math 160

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**Math 160**2.2/2.5 – Graphs and Transformations of Functions**Ex 1.**Graph .**Ex 1.**Graph .**Ex 1.**Graph .**Ex 1.**Graph .**Ex 1.**Graph .**Ex 1.**Graph .**Ex 1.**Graph .**Ex 1.**Graph .**Ex 1.**Graph .**Ex 1.**Graph .**Ex 1.**Graph .**Ex 1.**Graph .**Ex 1.**Graph .**Ex 1.**Graph .**Ex 2.**Graph .**Ex 2.**Graph .**Ex 2.**Graph .**Ex 2.**Graph .**Ex 2.**Graph .**Ex 2.**Graph .**Ex 2.**Graph .**Ex 2.**Graph .**Ex 2.**Graph .**Ex 2.**Graph .**Ex 2.**Graph .**Ex 2.**Graph .**Ex 2.**Graph .**Ex 2.**Graph .**Ex 2.**Graph .**Ex 2.**Graph .**Ex 2.**Graph .**Transformations of Functions**For a function , and , shifts up shifts down stretches vertically (if ), or shrinks vertically (if ) reflects about -axis shifts right shifts left stretches horizontally (if , or shrink horizontally (if ) reflects about -axis**Transformations of Functions**For a function , and , shifts up shifts down stretches vertically (if ), or shrinks vertically (if ) reflects about -axis shifts right shifts left stretches horizontally (if , or shrink horizontally (if ) reflects about -axis**Transformations of Functions**For a function , and , shifts up shifts down stretches vertically (if ), or shrinks vertically (if ) reflects about -axis shifts right shifts left stretches horizontally (if , or shrink horizontally (if ) reflects about -axis**Note: To graph a transformed function, plot key points of**basic function and then move points based on transformations. Typically, order of transformations is: 1. Horizontal stretch/shrink/reflect 2. Horizontal shift 3. Vertical stretch/shrink/reflect 4. Vertical shift**Ex 3.**Graph .**Ex 3.**Graph .**Ex 3.**Graph .**Ex 3.**Graph .