Pearson Algebra 1 Common Core, 2011
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Pearson Algebra 1 Common Core, 2011 View details
3. Patterns and Nonlinear Functions
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Exercise 22 Page 251

Compare the characteristics of the given function with those of a general linear function.

Answer: Nonlinear
Explanation: See solution.

Practice makes perfect

We are given the description of a function that, each time increases by the value of continually decreases by a smaller amount each time. Additionally, the value never reaches a value as low as Is this function is linear or not? Let's compare the characteristics of the given function with those of a general linear function.

  • Each time increases by the value of decreases by a smaller amount each time. Recall that the main characteristic for a linear function is that the change in compared to the change in is constant. As this is not the case here, this is NOT a linear function.
  • The function never reaches a value as low as The graph of a linear function is a line that continues on, passing through all values of and at some point. The exception to this is for cases where the line is horizontal or vertical, or has restrictions based on real-world scenarios. This is another clue confirming this is NOT a linear function.

As we can see, due to its characteristics, we know that the described function is nonlinear.