If `0 le t le 1`, which of the following graphs is the graph of y versus x where x and y are related by the parametric equations `y=t^(2)` and `x = sqrt(t)` ?

Options

A.
B.
C.
D.

Answer

C

Explanation

Combine the equations so as to lose t and get y in terms of x :
`x = sqrt(t)`
`x^(2)=t`
`y=t^(2)`
`y=(x^(2))^()=x^(4)`
So you might be tempted by (D), which looks like the graphs of `y = x^(4)`. But the stem says that `0 le t le 1`, so the only possible values of `x = sqrt(t)` are `0 le x le 1`, so the correct graph is (C ).