Write a function rule for the table.
| x | f(x) |
| --- | ---- |
| -1 | 0 |
| 0 | 1 |
| 1 | 2 |
| 2 | 3 |
A. [tex]f(x)=x[/tex]
B. [tex]f(x)=x+1[/tex]
C. [tex]f(x)=x-1[/tex]
Answer (2)
Test f ( x ) = x : It does not fit the table since f ( − 1 ) = − 1 e q 0 .
Test f ( x ) = x + 1 : It fits the table since f ( − 1 ) = 0 , f ( 0 ) = 1 , f ( 1 ) = 2 , and f ( 2 ) = 3 .
Test f ( x ) = x − 1 : It does not fit the table since f ( − 1 ) = − 2 e q 0 .
The function rule is f ( x ) = x + 1 .
Explanation
Understanding the Problem We are given a table of x and f ( x ) values and asked to find the function rule that describes the relationship between x and f ( x ) . We will test each of the given options to see which one fits the data in the table.
Testing the first option Let's test the first option, f ( x ) = x .
When x = − 1 , f ( x ) = − 1 , but the table shows f ( − 1 ) = 0 . So, f ( x ) = x is not the correct function rule.
Testing the second option Now let's test the second option, f ( x ) = x + 1 .
When x = − 1 , f ( x ) = − 1 + 1 = 0 .
When x = 0 , f ( x ) = 0 + 1 = 1 .
When x = 1 , f ( x ) = 1 + 1 = 2 .
When x = 2 , f ( x ) = 2 + 1 = 3 .
This function rule matches all the values in the table.
Testing the third option Finally, let's test the third option, f ( x ) = x − 1 .
When x = − 1 , f ( x ) = − 1 − 1 = − 2 , but the table shows f ( − 1 ) = 0 . So, f ( x ) = x − 1 is not the correct function rule.
Conclusion Therefore, the correct function rule is f ( x ) = x + 1 .
Examples
In real life, function rules can be used to model various relationships. For example, if you earn 10 p er h o u r , t h e f u n c t i o n r u l ere l a t in g yo u re a r nin g s E t o t h e n u mb ero f h o u rsyo u w or k h i s E(h) = 10h$. Similarly, if you have an initial amount of money and save a fixed amount each week, a function rule can describe your total savings over time. Understanding function rules helps in predicting outcomes and making informed decisions based on the relationship between variables.
The correct function rule based on the table is f ( x ) = x + 1 , as it accurately matches all given values. The other options do not fit the data correctly. Therefore, the answer is option B: f ( x ) = x + 1 .
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