Q. 11. - Calculus

Question

Explain how to use parametric equations to transform the

function $y=f\left(x\right)$

Step-by-Step Solution

Answer

The parametric equations are $x=t, y=f\left(t\right)$

Step 1: Given information

The function is $y=f\left(x\right)$where $y$ is explicitly expressed as a function of $x$

This is not a straightforward representation of every curve.

To get around this problem, each variable is stated as a function of a new variable called a parameter.

Step 2: The objective is to explain how to use parametric equations to transform the function y = f ( x )  

For the function $y=f\left(x\right)$allowing $x=t$ is one technique to get parametric equations then $y=f\left(t\right)$and $x\left(t\right)=t, y\left(t\right)=f\left(t\right)$where $t$ is in the domain of $f$, are parametric equations of the curve.

Hence, the parametric equations are

$x=t, y=f\left(t\right)$