Question

Susan's cell phone plan includes unlimited texting. The amount she pays for texting each

month can be described by the function y = 20, where y is the number of dollars spent on
texting as a function of x, the number of texts.
What is true about the function?
It is linear because the rate of change is zero.
It is linear because the rate of change is increasing.
It is nonlinear because the rate of change is zero.
It is nonlinear because the rate of change is
increasing.

Answer 1

The function y = 20, where y is the number of dollars spent on texting as a function of x, the number of texts, is a linear function. This is because the function has a constant rate of change, which is zero. [ For any increase in the number of texts, the amount spent on texting remains the same at $20 per month. A linear function has a constant rate of change, which means that the slope of the line is constant. Therefore, the function y = 20 is linear, and not nonlinear. Additionally, the rate of change is not increasing since it remains constant, so the answer is "It is linear because the rate of change is zero." ]