1. Properties of Functions
How are Functions Evaluated?
Section 2.1
Properties of Functions

2. How are Functions Evaluated?

3. Does this Represent a Function?
How are Functions Evaluated?

4. Identify the Domain and Range
How are Functions Evaluated?

5. Find the Domain and Range for the Function below
Solution: The domain includes only those values of x satisfying since the denominator cannot be zero. Using the methods for solving a quadratic inequality produces the domain Because the numerator can never be zero, the denominator can take on any positive real number except for 0, allowing y to take on any positive value except for 0, so the range is
How are Functions Evaluated?

6. Find the Domain and Range for the Function below
Solution: The domain includes only those values of x satisfying since the denominator cannot be zero. Using the methods for solving a quadratic inequality produces the domain Because the numerator can never be zero, the denominator can take on any positive real number except for 0, allowing y to take on any positive value except for 0, so the range is
How are Functions Evaluated?

7. How are Functions Evaluated?
Assessment Prompt #1
One’s do page 54 #7, 17, 27
Two’s do page 54 #5, 19, 25
Check each other’s work.
Be ready to share out.
How are Functions Evaluated?

8. How are Functions Evaluated?
Substitution
Given the function find each of the following. (a) (b) All values of x such that (a) Solution: Replace x with the expression x + h and simplify. (b) Solution: Set f (x) equal to − 5 and then add 5 to both sides to make one side equal to 0. Continued
How are Functions Evaluated?

9. Substitution continued
(b) Solution: Set f (x) equal to − 5 and then add 5 to both sides to make one side equal to 0.
How are Functions Evaluated?

10. Are these graphs functions?
How are Functions Evaluated?

11. How are Functions Evaluated?
Assessment Prompt #2
One’s do page 55 #41, 49, 71
Two’s do page 55 #43, 47, 71
Check each other’s work.
Be ready to share out.
How are Functions Evaluated?

12. How are Functions Evaluated?
Lesson Assignment
Explain how to find f(250 + x) for the function f(x) = 3x -5.
How are Functions Evaluated?

13. How are Functions Evaluated?
Page #4-32 every other even
and #44-80 every other even
Homework
How are Functions Evaluated?