Question

A certain function fits the following description: As the value of x increases by 1 each time, the value of y continually decreases by a smaller amount each time, and never reaches a value as low as 1. Is this function linear or nonlinear? Explain your reasoning

Answer 1

Answer:

non linear function

Step-by-step explanation:

given that a certain function fits the following description:

As the value of x increases by 1 each time, the value of y continually decreases by a smaller amount each time, and never reaches a value as low as 1.

This implies that for a unit increase in x, there is a decrease in y but the rate of change of y is not constant.  It steadily decreases upto 1 but not equals 1.

i.e. dy/dx limits to 1.

But for linear relationships we know that rate of change of y with respect to x should be a constant.  

Since here this function has slope constantly changing, this is not a linear function.

Non linear funciton is the answer.