This document discusses functions and their transformations. It introduces the basic linear function y=mx+b, and how changing the slope m or y-intercept b affects the graph. It then demonstrates how transformations like shifting the graph along the x- or y-axis, stretching or shrinking, and reflections change the function. Finally, it briefly covers quadratic, cubic, logarithmic, and exponential functions, and challenges the reader to match equation and graph.

1. Graphing Functions and Their TransformationsBy: Chris Zachow

2. The Basic Liney=mx+bm – the slope of the graph.

3. x – the place on the x axis.

4. b – the position on the y axisThe Basic Liney=mx+b

5. The Basic LineB changesy=1x+2

6. The Basic LineM changesy=2x+0

7. The Basic LineMoving on the x-axisy=(x+2)+0The graph moves to the left 2 points

8. The Basic LineCombining changesy=2(x-1)-2The graph moves to the right 1 points and down 2 points

9. Matchingy=xy=x+2y=2(x+2)y=-1(x-2)

10. Other Graphsx2

11. x3

12. logx

13. exParabolay=x2

14. Other Graphsy=x3

15. Other Graphsy=logx

16. Other Graphsy=ex