We are given the description of a function that, each time x increases by 1, the value of y continually decreases by a smaller amount each time. Additionally, the y-value never reaches a value as low as 1. 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 x increases by 1, the value of y decreases by a smaller amount each time. Recall that the main characteristic for a linear function is that the change in y compared to the change in x is constant. As this is not the case here, this is NOT a linear function.
The function never reaches a value as low as 1. The graph of a linear function is a line that continues on, passing through all values of x and y 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.
