1. Evaluating Functions and Operations on Functions
4 January 2011

2. Function Notation y = x2 – 4 f(x) = x2 – 4 Pronounced f of x
Identifies the equation as a function
Indicates which variable the function is in terms of (the variable used in the function)

3. Evaluating Functions Algebraically
Solve for the value of a function at a point.
f(x) = 2x – 10; find f(6)
f(6) = 2(6) – 10
f(6) = 12 – 10
f(6) = 2
The value of x is 6. Replace x with 6 and solve.

4. Evaluating Functions Algebraically, cont.
You can also evaluate functions with an expression
f(x) = 2x – 10; find f(x+1)
f(x+1) = 2(x+1) – 10
f(x+1) = 2x + 2 – 10
f(x+1) = 2x – 8

5. Your Turn
Complete problems 1 – 6 on the Evaluating Functions handout

6. Solving for the Domain of Functions Algebraically
Domain Convention – unless otherwise stated, the domain (input or x-value) of a function is every number that produces a real output (y-value)
No imaginary numbers or discontinuities!

7. Solving for the Domain of Functions Algebraically, cont.
Always identify where the function equals a discontinuity or an imaginary number. Then solve for the values of x that don’t occur at those points.

8. Example #1
Find the domain of f(x).

9. Example #2
Find the domain of f(x).

10. Example #3
Find the domain of f(x).

11. Your Turn:
Complete problems 7 – 14 on the Evaluating Functions handout

12. Evaluating Functions Graphically
y = x2 – 4 f(x) = x2 – 4
Find f(2) means
find the value of
y when x = 2.

13. Your Turn:
Complete problems 15 – 18 on the Evaluating Functions handout

14. Operations on Functions
We can add, subtract, multiply and divide functions