These are two questions and two answers.
Question 1. The ordered pair given in the first row in the table can be written using function notation as?
Answer: f(-2) = 1
Justification:
In functions, the notation f(x) denotes the image (ouput) obtained when you apply the rule (function) to the value x, i.e. x is the input.
So, for example, the image of x = 5 is f(5), the image of x = 2,000 is f(2,000), the imaga of x = - 100.5 is f(-100.5).
In the table, the first row shows that the image of x = -2 is 1, so f(-2) = 1, and that is the answer to the question.
Question 2. f(x) = –2 when x is?
Answer: x = 4.
Justification.
You are requested to find which value of x makes the function f(x) equals -2.
Therefore, you have to see that in the third row of the table it is shown that f(x) is - 2 when x = 4., and that is the answer.
All the following expressions mean the same and are used when you deal with functions:
- the ordered pair (4, -2),
- the image of 4 is - 2
- the preimage of -2 is 4
- f(4) = -2
- f(x) = -2, when x = 4.