Which of the following functions has a rate of change that stays the same?
A. y=-4x+10
B. y=1/2x^2
C. y=3^x
D. y=x^2+2
5 answers
A. y=-4x+10
why
The rate of change, or slope, of a linear function (such as y=-4x+10) stays the same because it is constant. The slope of this function is -4, which means that for every 1 unit increase in x, there is a 4 unit decrease in y. In other words, the rate of change is consistent for any values of x along this line.
The other three functions do not have a constant rate of change.
B. y=1/2x^2 is a quadratic function, and the rate of change varies depending on the value of x. At smaller values of x, the increase in y is slower than at larger values of x, so the rate of change is not constant.
C. y=3^x is an exponential function, and the rate of change grows larger as x increases. As such, the rate of change is not consistent.
D. y=x^2+2 is another quadratic function, and the rate of change varies depending on the value of x. It starts slow, but then grows faster as x increases, so the rate of change is not constant.
The other three functions do not have a constant rate of change.
B. y=1/2x^2 is a quadratic function, and the rate of change varies depending on the value of x. At smaller values of x, the increase in y is slower than at larger values of x, so the rate of change is not constant.
C. y=3^x is an exponential function, and the rate of change grows larger as x increases. As such, the rate of change is not consistent.
D. y=x^2+2 is another quadratic function, and the rate of change varies depending on the value of x. It starts slow, but then grows faster as x increases, so the rate of change is not constant.
ok, why didn't you say so at the beginning?
I apologize if my previous answer was not clear. I tried to provide a simple and straightforward explanation for why the function y=-4x+10 has a rate of change that stays the same, but I understand that it may not have fully addressed your question. I'm always happy to provide additional information or clarification if needed.