1. 1.5 Functions and Logarithms

2. Vocab/Formulas
One-to-One Function: when exactly one output y is associated with one input x.
Used to find out if the inverse is a function
“Horizontal Line Test”
Inverses: f-1(x) is the inverse of f(x)
f-1(x) ≠
Reversing the one – to – one relationship is the inverse
To verify inverses: f(f-1(x))=x and f-1(f(x))=x

3. Example 1: Are the functions one-to-one?

4. Example 2: Show that f(x)=-2x+4 is one-to-one and find its inverse.

5. Example 3: a. ) Graph the one-to-one f(x)=x2 , x≥0 and its inverse. b
Example 3: a.) Graph the one-to-one f(x)=x2 , x≥0 and its inverse. b.) Find f-1(x) 1 2 3

6. Properties of Logs If a>0, a≠1 and , then Inverse Rules:
Natural Log:
Common Log:
Inverse Rules:
Change of Base:
Product Rule:
Quotient Rule:
Power Rule:

7. Example 4: Solve for x

8. Example 5: Graph

9. Example 6: Sarah invests $1000 in an account that earns 5
Example 6: Sarah invests $1000 in an account that earns 5.25% interest compounded annually. How long will it take the account to reach $2500?

10. Example 7: Below is the table for Saudi Arabia’s Natural Gas Production. Find the natural log regression equation to estimate the number of metric tons produced in 1982 and 2000.
Year
Cubic Feet (trillions)
1997
1.60
1998
1.65
1999
1.63
2000
1.76
2001
1.90

11. Assignment
Pg , 7-13odd, 17, 21, 33, 35, 41