Math Problem Statement
The table shows a function. Is the function linear or nonlinear based on the values provided?
Solution
Let's analyze the table shown in your image to determine if the function is linear or nonlinear. The table lists values for and as follows:
\hline x & y \\ \hline 15 & 2 \\ 16 & 9 \\ 17 & 15 \\ \hline \end{array}$$ To determine if a function is linear, the change in $$y$$ must be constant for a constant change in $$x$$. In other words, if the difference between successive $$x$$ values is always the same, and the same is true for the differences in corresponding $$y$$ values, the function is linear. ### Step 1: Calculate the change in $$x$$ - From 15 to 16, $$\Delta x = 16 - 15 = 1$$ - From 16 to 17, $$\Delta x = 17 - 16 = 1$$ ### Step 2: Calculate the change in $$y$$ - From 2 to 9, $$\Delta y = 9 - 2 = 7$$ - From 9 to 15, $$\Delta y = 15 - 9 = 6$$ The changes in $$y$$ are not constant ($$7 \neq 6$$), even though the changes in $$x$$ are constant. This indicates that the function is **nonlinear**. Would you like further details on why the function is nonlinear or have any other questions? Here are 5 related questions to explore this topic further: 1. How do you find the equation of a linear function from a table? 2. What are the characteristics of a nonlinear function? 3. Can nonlinear functions ever be modeled with an equation? 4. How does the rate of change help identify a linear function? 5. What are examples of common nonlinear functions? **Tip:** A function is linear if its graph forms a straight line, and the rate of change between any two points is constant.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Functions
Linear and Nonlinear Functions
Rate of Change
Formulas
Change in y / Change in x
Theorems
Linear Function Criteria
Suitable Grade Level
Grades 6-8