Find a function fx whose graph is the curve ct Find a functi

Find a function f(x) whose graph is the curve c(t)

Find a function f(x) whose graph is the curve c(t) = (t - 2)i + t^4j. f(x) = .

Solution

The curve is given by C(t) = ( t - 2) i + t⁴j

Let x = t - 2 and y = t⁴ then t = x + 2  

Since we have y = t⁴ = ( x + 4 )^4.

Hence the required function is y = f(x) = ( x + 4 )⁴