Math Problem Statement
which one
Which table below represents a linear function?
Solution
To determine which table represents a linear function, we need to check if the relationship between and values is consistent with a linear pattern. A linear function has a constant rate of change between consecutive values of and .
Let’s evaluate both tables:
Table A:
\hline x & -2 & 0 & 2 & 4 \\ \hline y & -1 & 0 & 1 & 2 \\ \hline \end{array}$$ Calculate the differences in $$y$$-values between consecutive $$x$$-values: - From $$x = -2$$ to $$x = 0$$, $$y$$ changes from -1 to 0, a difference of 1. - From $$x = 0$$ to $$x = 2$$, $$y$$ changes from 0 to 1, a difference of 1. - From $$x = 2$$ to $$x = 4$$, $$y$$ changes from 1 to 2, a difference of 1. The difference is constant, which suggests this is a linear function. **Table B:** $$\begin{array}{|c|c|c|c|c|} \hline x & 1 & 2 & 3 & 4 \\ \hline y & 1 & 4 & 9 & 16 \\ \hline \end{array}$$ Calculate the differences in $$y$$-values between consecutive $$x$$-values: - From $$x = 1$$ to $$x = 2$$, $$y$$ changes from 1 to 4, a difference of 3. - From $$x = 2$$ to $$x = 3$$, $$y$$ changes from 4 to 9, a difference of 5. - From $$x = 3$$ to $$x = 4$$, $$y$$ changes from 9 to 16, a difference of 7. The differences are not constant, meaning this is not a linear function. ### Conclusion: **Table A** represents a linear function because the differences in the $$y$$-values are consistent. Would you like further clarification on this? Let me know if you'd like to go into more detail! Here are five related questions: 1. How do you determine the slope of a linear function from a table? 2. What other types of functions can be identified from tables of values? 3. How can you graph a linear function from a table of values? 4. How do you find the equation of a linear function given a set of points? 5. What is the difference between a linear function and a quadratic function? Tip: Always check the differences between consecutive $$y$$-values in a table to determine if the function is linear.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Linear Functions
Rate of Change
Algebra
Formulas
Slope formula: (y2 - y1) / (x2 - x1)
Theorems
Concept of Constant Rate of Change
Suitable Grade Level
Grades 7-9