Evaluation of a function
A function of a real variable is a rule of correspondence that associates one real number to another real number (and only one other number) commonly referred to as its image.
Notation y = f(x)
Example 1
Calculate the images of 2, -3, a, and x+h following the rule f(x) = 2x - 1
Solution f(2) = 2×2 -1 = 3
f(-3) = 2×(-3) - 1 = -7
f(a) = 2a - 1
f(x + h) = 2(x + h) - 1
Example 2
Given the function f(x) =
,
calculate the images of -2, 1 and x+h
Solution
f(-2) = 
= 
= 
f(1) = 
is not defined because division by 0 is impossible.
f(x+h) = 
Example 3
Given f(x) = 
x
- 1,
calculate the images of 5, 0, 10, 1.
Solution
f(5) = 5 - 1 = 2
f(0) does not exist because the square root of a negative number is undefined.
f(10) = 10
- 1 = 3 and
f(1) = 1 - 1 = 0
Before proceeding to the questions, ensure that you have a pencil and some
paper handy.
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