What is the unit of this "Rate of Change"?the function f ( x ) = 0.9 xSo, the rate of change of y with respect to x is 0.9.My question is, what is the unit of this Rate of Change?0.9 per x?

Question

What is the unit of this &quot;Rate of Change&quot;?the function   f  (  x  )  =  0.9  xSo, the rate of change of y with respect to x is 0.9.My question is, what is the unit of this Rate of Change?0.9 per x?

cindysnifflesuz · Accepted Answer

Well, it really depends on context. In a very pure sense, the slope does not have units in this context. In a more vernacular sense, it&#039;s common to have things like  y  =  # of meters travelled of meters travelled  x  =  # of seconds passed of seconds passedThen write y=2x as a relationship. Then, the units of slope would be meters/second, meaning that two meters pass (on the y-axis) for every one second on the x-axis. So, the units here are the units of the y-axis divided by those of the x-axis.However, it&#039;s worth noting that this relationship might be better written as  f  (  x   seconds  )  =  2  x   meterswhere you recognize that the function f takes in a duration and spits out a length - and that the units are not an intrinsic quality of the function. In this sense, you could justifiably write for the same function that  f  (      x    ′     minutes  )  =  120      x    ′     meters  .An equivalent way to write this function is as follows:  f  (  t  )  =  (  2   meters/second  )  ⋅  twhere you note that if you plug in x seconds for t, you get 2x meters. This last point of view shows that the slope is just the coefficient multiplied by the input - and it is very often desirable to treat these slopes as intrinsically having units which are part of the value, not an interpretation thereof.In an abstract setting (or a setting where the input and output are both distances or both times or generally both the same), the slope does not have units. It is just 0.9.

Graham Beasley · Accepted Answer

If you would put units for x and y, say time in seconds for x and distance in meters for y, the slope is in meters/second. So in the general case, the unit for the rate of change is &quot;units of y divided by units of x&quot;. You can use &quot;per&quot; instead of &quot;divided by&quot;.

What is the unit of this "Rate of Change"? This is the plot of the function f(x)=0.9x. So, the rate of change of y with respect to x is 0.9. My question is, what is the unit of this Rate of Change? 0.9 per x?

Answered question

Answer & Explanation

New Questions in Calculus 2