Transformations of Functions I. There are 4 basic transformations for a function f(x). y = A • f (Bx + C) + D A) f(x) + D (moves the graph + ↑ and – ↓) B) A • f(x) (this is the “slope” of the function) 1) If | A | > 1 then it is vertically stretched. 2) If 0 < | A | < 1, then it’s a vertical shrink. 3) If A is negative, then it flips over the x-axis. C) f(x + C) (moves the graph  + and – ) D) f(Bx) or f(B(x)) (sometimes we factor out the B term) 1) If | B | > 1 then it’s a horizontal shrink. 2) If 0 < | B | < 1, then it’s horizontally stretched. 3) If B is negative, then it flips over the y-axis.

Transformations of Functions II. What each transformation does to the graph. A) f(x) f(x) + D f(x) – D B) +A f(x) +A f(x) –A f(x) . A > 1 0 < A < 1

Transformations of Functions II. What each transformation does to the graph. C) f(x) f(x + C) f(x – C) D) f(Bx) f(Bx) f(-Bx) . B > 1 0 < B < 1

Transformations of Functions III. Finding min, max & zeroes on the calculator. A) On the Home screen, go to the bottom blue graph icon. 1) Type in your equation into f1(x) and press enter. B) Press menu and scroll to 6: Analyze Graph 1) Pick 2: Minimum or 3: Maximum a) Move the cursor to the left of the min/max & enter, b) Move the cursor to the right of min/max & enter. 2) Pick 1:Zero to find the x-intercepts a) Move the cursor to the left of any x-int & enter, b) Move the cursor to the right of that x-int & enter.