QQuestionMathematics
QuestionMathematics
Which table represents a linear function?
| $x$ | $y$ |
| --- | --- |
| 1 | 1 |
| 1 | 2 |
| 2 | 1 |
| 3 | $1 \frac{1}{2}$ |
| 4 | 2 |
| $x$ | $y$ |
| --- | --- |
| 1 | 1 |
| 2 | 1 |
| 2 | 2 |
| 3 | 1 |
| 3 | 3 |
| 4 | 1 |
| 4 | 4 |
| $x$ | $y$ |
| --- | --- |
| 1 | 7 |
| 2 | 9 |
| 3 | 13 |
| 4 | 21 |
| $x$ | $y$ |
| --- | --- |
| 1 | 0 |
| 2 | 6 |
| 3 | 16 |
| 4 | 30 |
12 months agoReport content
Answer
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Step 1:Let's solve this step by step:
Step 2:: Recall the definition of a linear function
- $$b$$ is the y-intercept
- m is the slope (constant rate of change)
Step 3:: Check the first table
- This table is NOT linear because for $$x = 1$$, we have two different $$y$$ values (1 and 2)
- A linear function requires each x value to have only one corresponding y value
Step 4:: Check the second table
- This table is also NOT linear because for $$x = 2$$ and
x = 3, there are multiple y values - This violates the definition of a function
Step 5:: Check the third table
x = 4$$: $$21 - 13 = 8
- From x = 1 to - The differences are not constant, so this is NOT a linear function
Step 6:: Check the fourth table
x = 4$$: $$30 - 16 = 14
- From x = 1 to - These differences are increasing, suggesting a quadratic relationship
Final Answer
None of the tables represent a linear function.
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