Transcript PPadua-Douglas,E. HMWK 2012-02-08 10450

February 7, 2012
At the end of today, you will understand
exponential functions and their
transformations.
Warm-up: Correct HW 4.7
1. π/6
13. π/3
3. π/3
15. 0
5. π/6
49. 3/5
7. 5π/6
51. √5/5
9. -π/3
53. 12/13
11. 2π/3
55. √34/5
57. √5/3
59. 1/x
61. 1 4x 2
63. 1 x 2


3.1 Graphing Exponential
Equations
An exponential equation looks like…
y = bx
… where b is any number (the base) and the
variable x is in the exponent
Get a calculator and graph y = 2x
Points on the Graph
X
y
0
1
1
2
2
4
How do you find these points in your calculator?
Graph of y =
x
2
Important parts of the graph
X
Y
-3
1/8
-2
1/4
-1
1/2
0
1
1
2
Y approaches 0
2
4
3
8
What happens to
y as x gets more
negative?
Y goes to ∞
What happens to
y as x gets more
positive?
Graph of y = 2x
Does the graph ever touch the x-axis?
(Does y ever = 0?)
– No! So, the x-axis is called an asymptote of
the graph
– An asymptote is an imaginary line that your
graph gets infinitely close to, but never
touches!
What is the Domain and Range?
– Domain: All real numbers
– Range: y > 0
Classwork
• Graph each exponential function and make sure
to plot at least 3 points on your graph.
• When you plug in y = 2x + 1, make sure you type
in y = 2^(x+1) ---use parentheses.
• Define each transformation by comparing it to
the parent function y = 2x.
• 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 1722, make sure you compare it to the first function
it gives you.