Pre Calculus notes 4 1 Exponential Functions
- 1. l Note s 4 -1 PreC a IICK K ctions L C !!! C L !!! ial Fun C E ME one nt M Exp
- 3. Definition: Exponential Function The exponential function with base a is defined by: f(x) = ax where a > 0 and a ≠ 1.
- 4. Ex 1—Evaluating Exponential Functions Let f(x) = 3x and evaluate the following: (a) f(2) = 32 = 3 ^ 2 ENTER = 9 (b) f(–⅔) = 3-⅔ =3 ^((–) 2÷3 ) ENTER ≈ 0.4807 (c) f(π) = 3π = 3^π ENTER ≈ 31.544 (d) f( √2 ) = 3√2 = 3^√ 2) ENTER ≈ 4.7288 Hint: you will need a calculator!!
- 5. Graphs of Exponential Functions F(x) = ax Domain: All real numbers Range: (0, ∞)
- 6. ex 2: Identifying Graphs of Exponential Functions Find the exponential function f(x) = ax whose graph is given. Since f(2) = a2 = 25, we see that the base is 5. SO… f (x) = 5x
- 7. ex 3: Identifying Graphs of Exponential Functions Find the exponential function f(x) = ax whose graph is given. Since f(3) = a3 = 1/8 , we see that the base is ½ . SO... f (x) = (½)x
- 8. reak ! !!! Brain B
- 9. Speaking of Infinity… Make an infinity symbol with your right hand out in front of you. and stop your finger on the far right side of the infinity sign. Lift your left hand to be at the far left side of the infinity sign. Now move your hands at the same time and the same pace in the same direction to continue your infinity sign. Your hands should cross the middle at the same time. This one seems easy at first. Then you try to do it when your hands are doing the infinity signs in different directions. You should look like a choir director if you are doing it correctly.
- 10. We can graph Exponential Functions using transformations. Find the parent function f(x) = 2x in the front of your book.
- 11. Ex4—Transformations Use the graph of f(x) = 2x to sketch the graph of the function. g(x) = 1 + 2x Notice that the line y = 1 is now a horizontal asymptote.
- 12. Ex5 - Use the graph of f(x) = 2x to sketch the graph of the function. h(x) = –2x
- 13. EX 6: Use the graph of f(x) = 2x to sketch the graph of the function. k(x) = 2x –1
- 14. You have finished your Homework!! Great job! Now go get a cookie for yourself! ;)