Average Rate of Change for Parametric Functions

Question

The table shows values for a parametrically defined function with x(t) = t^2 and y(t) = sin(t). Which of the following parametric functions has an average rate of change of y with respect to x that is equal to its average rate of change of y with respect to t?

TABLE:

t	x(t)=t^2	y(t)=sin(t)
1	1	sin(1)
2	4	sin(2)
3	9	sin(3)

TABLE:
|  t  | x(t)=t^2 | y(t)=sin(t) |
|-----|----------|------------|
|  1  |    1     |   sin(1)   |
|  2  |    4     |   sin(2)   |
|  3  |    9     |   sin(3)   |

Accepted Answer

$$f(t) = (t^2,\ \sin(t))$$

Answer

$$y = t^2$$

Answer

$$f(t) = (t,\ \sin(t))$$

Answer

$$f(t) = (\cos(t),\ \sin(t))$$

Average Rate of Change for Parametric Functions

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