1. February 7, 2012 At the end of today, you will understand exponential functions and their transformations. Warm-up: Correct HW 4.7 1. π/613. π/357. √5/3 3.π/315. 059. 1/x 5.π/649. 3/561. 7.5π/651. √5/563. 9.-π/353. 12/13 11. 2π/355. √34/5

2. 3.1 Graphing Exponential Equations An exponential equation looks like… y = b x … where b is any number (the base) and the variable x is in the exponent Get a calculator and graph y = 2 x Points on the Graph X y 0 1 1 2 2 4 How do you find these points in your calculator?

3. Graph of y = 2 x Important parts of the graph XY -3 -2 0 1 2 3 What happens to y as x gets more negative? What happens to y as x gets more positive? Y approaches 0Y goes to ∞ 1/8 1/4 1/2 1 2 4 8

4. Graph of y = 2 x Does the graph ever touch the x-axis? (Does y ever = 0?) –N–No! So, the x-axis is called an asymptote of the graph –A–An asymptote is an imaginary line that your graph gets infinitely close to, but never touches! What is the Domain and Range? –D–Domain: All real numbers –R–Range: y > 0

5. Classwork Graph each exponential function and make sure to plot at least 3 points on your graph. When you plug in y = 2 x + 1, make sure you type in y = 2^(x+1) ---use parentheses. Define each transformation by comparing it to the parent function y = 2 x. Write out the rule for each transformation. When you are done, have me check out the rules you made for each transformation. Then start HW 3.1: Pg. 226 #7-22. For #s 17- 22, make sure you compare it to the first function it gives you.