Functions and Graphs
Function Notation
Example
For the function f(x) = 4x^{2}  5x + 10, find:
a. f(3)
b. f(2)
c. f(a)
Solution
a. To calculate f(3) means to find the value of the function when the
input variable has a value of 3. That is, substitute 3 for x and then
simplify:
a. 
Original function.
Substitute 3 for x.
Multiply.
Add and subtract. 
f(x)
f(3) 
= 4x^{2}  5x + 10 = 4(3)^{2}
 5(3) + 10
= 36  15 + 10
= 31 
So, when x = 3, the value of the function is 31. That is, f(3) = 31.
This can be written as the ordered pair (3, 31).
b. 
Original function.
Substitute 2 for x.
Multiply.
Add. 
f(x)
f(2) 
= 4x^{2}  5x + 10 = 4(2)^{2}
 5(2) + 10
= 16 + 10 + 10
= 36

So, when x = 2, the value of the function is 36. That is, f(2) = 36.
This can be written as the ordered pair (2, 36).
c. 
Original function.
Substitute a for x.
Simplify. 
f(x)
f(a) 
= 4x^{2}  5x + 10 = 4(a)^{2}
 5(a) + 10
= 4a^{2}  5a + 10

Since we do not know the value of a, we cannot simplify this further.
