1. and a review of scientific notation 2.7 – Piecewice Functions

2. SCIENTIFIC NOTATION Used to write very, very small or very, very large numbers. In the form of c stands for any real number between 1 and 10 n stands for any integer Examples: 5.2 x 10 12 and 7.13 x 10 -15

3. Writing Numbers in Standard Form The exponent tells you how many places to move the decimal Positive means to the right Negative means to the left Fill in the empty places with zeros. Example: 4.38 x 10 8 = 438,000,000. 7.05 x 10 -4 = 0.000705

4. Your Turn! Write each number in standard form 1. 6.14 x 10 11 2. 8.245 x 10 -7

5. Writing Numbers in Scientific Notation Just the opposite of writing numbers in standard form 1 st move your decimal behind the first number and write all numbers except the zeros at the end 2 nd count the number of places you moved your decimal 3 rd write your new number “times 10 to the power of n” n is the number of places you moved your decimal If the original number was bigger than one, your exponent is positive If the original number was smaller than one, your exponent is negative

6. Write the following numbers in scientific notation 1. 83,000,000 2. 704,000,000,000 3. 0.00000451 4. 0.00000000729

7. What is a Piecewise Function? A combination of equation with their own domain. Example: If you were putting in a number smaller than 2, you would use the first equation. If you were putting in a number larger than or equal to 2, you would use the second equation.

8. Evaluate f(x) for the given values 1. Let. Evaluate f(0), f(3), and f(6).

9. Evaluate f(x) for the given values 1. Let Evaluate f(-1), f(2), and f(4).

10. Evaluate the function. 1. g(6) 2. g(-3)

11. Graphing Piecewise Functions 1. Evaluate equation # 1 at 2 points (1 point being where the 2 functions separate) 2. Graph the first line with an open or closed dot. 3. Repeat these steps to graph line #2.

12. Graph the piecewise function

13. Shipping costs $6 on purchases up to $50, $8 on purchases over $50 and up to $100, and $10 on purchases over $100 and up to $200. Write a piecewise function for these charges. Graph the function. State the domain and range.