1. -4 is the y-value or the function value.
Function: Evaluating
Example 1: Given f (x) = 5 – x2, find f (- 3).
The notation f (- 3) means to replace the independent variable, x with - 3 and calculate the value of the dependent (or function) variable, y.
So here,
f (- 3)
= 5 – (- 3)2
= 5 - 9
= - 4
-4 is the y-value or the function value.

2. Function: Evaluating
Example 2: Given f (x) = (x – 4)2, find f (a).
Here, replace x with a:
f (a)
= (a – 4)2
= a2 – 8a
In this case a numerical y- or functional-value has not been found. However, a formula for it in terms of a has been found.

3. Here f (a + h) means to replace x with a + h so
Function: Evaluating
Example 3: Given f (x) = x x, find f (a + h) – f (a).
Here f (a + h) means to replace x with a + h so
f (a + h) = (a + h) (a + h)
f (a + h) = a ah + h a + 2h
f (a) means to replace x with a so
f (a) = a a

4. Function: Evaluating
Example 3: Given f (x) = x x, find f (a + h) – f (a).
To find f (a + h) – f (a), subtract the resulting expressions to get
(a ah + h a + 2h) – (a a)
= a ah + h a + 2h – a2 – 2a
= 2ah + h h
So f (a + h) – f (a) = 2ah + h h.
Here, the difference between the y-value when x = a + h and the y-value when x = a has been found.

5. Function: Evaluating
Example 4: Given find f (2).
This function is defined in two pieces. One piece is f (x) = x2. It is defined only for x-values that are  3.
The other piece is f (x) = x It is defined only for x-values that are > 3.
Since the function is being evaluated for x = 2 and 2  3, the top piece f (x) = x2 is used.
Therefore, f (2) = (2)2 = 4.

6. Function: Evaluating
END OF PRESENTATION