1. Ch. 1 – Functions and Their Graphs 1.4 – Shifting, Reflecting, and Sketching Graphs

2. Graphs of Common Functions Below are 6 common functions. They are in their most basic, or parent, form. Constant Function f(x) = c Linear Function f(x) = x Absolute Value Function f(x) = |x|

3. Graphs of Common Functions Square Root Function Quadratic Function f(x) = x 2 Cubic Function f(x) = x 3

4. Graphs of Common Functions Types of rigid transformations: ▫Vertical shift (moves c units up)  h(x) = f(x) + c ▫Horizontal shift (c units to the right)  h(x) = f(x – c) ▫Reflection across the x-axis  h(x) = -f(x) ▫Reflection across the y-axis  h(x) = f(-x)

5. Graphs of Common Functions Types of nonrigid transformations: Stretch/Shrink ▫h(x) = cf(x) ▫If |c |>1, then the graph is stretched by a factor of c ▫If |c |<1, then the graph is shrunk by a factor of c

6. When transforming a graph, start with the parent function and work inside out (OOO!) Ex: Graph the function y = (x – 2) 2 + 1 ▫ Parent function is y = x 2 ▫ First thing done to the x: –2 (a horizontal shift 2 units to the right) ▫ Next thing done to the x: +1 (a vertical shift 1 unit up) ▫ That’s it!

7. Ex: Graph the function y = -2(x + 1) 3 ▫ Parent function is y = x 3 ▫ First thing done to the x: +1 (a horizontal shift 1 unit to the left) ▫ Next thing done to the x: 2 (a vertical stretch 2 units) ▫ Last thing: the negative (flip the whole graph across the x-axis)

8. What function is graphed below? 1. 2. 3. 4.

9. What function is graphed below? 1. 2. 3. 4.