The table represents the function f(x).
What is f(3)?
X f(x) -3 -9 -6 -2 -1 0 1 2 3 -3 0 3 6 9
The Correct Answer and Explanation is :
To determine the value of ( f(3) ), you need to find the corresponding output for the input ( x = 3 ) from the table. Here’s the relevant section of the table:
| ( x ) | ( f(x) ) |
|---|---|
| -3 | -9 |
| -6 | -2 |
| -1 | 0 |
| 1 | 2 |
| 3 | -3 |
| 0 | 3 |
| 6 | 9 |
From this, when ( x = 3 ), the corresponding value of ( f(x) ) is:
[
f(3) = -3
]
Explanation (300 words):
The question asks us to find the value of ( f(3) ) from a table that represents a function ( f(x) ). A function is a relationship that assigns exactly one output (value of ( f(x) )) for each input (value of ( x )). This means that for every value of ( x ), there is a corresponding unique value of ( f(x) ).
In this table, each pair of ( x ) and ( f(x) ) represents an input-output relationship. To find ( f(3) ), we need to look at the row where ( x = 3 ). According to the table, when ( x ) equals 3, ( f(x) ) equals -3. Therefore, the value of the function at ( x = 3 ) is:
[
f(3) = -3
]
In more general terms, tables like this are used to represent discrete functions, where the function is defined only for specific values of ( x ). The table allows us to quickly find the output for any given input. Unlike formulas or equations that describe a continuous function, this type of table simply lists all possible input-output pairs.
Since this table is already provided and represents the exact outputs, there’s no need to perform any calculations—just look for the input value of 3 and read off the corresponding output value.
Hence, ( f(3) ) is -3, based on the information from the table.