Chapter 0, Problem 3RWDT

To determine

The graph of a function always be given in parametric form or not.

Answer to Problem 3RWDT

No, It is depends on the function.

Explanation of Solution

Given Information:

The statement is “Can the graph of a function always be given in parametric form?”.

Consider the given statement,

Suppose that a function is defined as,

  $f\left(x,y\right)=x^2+y^2$

So the above function can draw without using parametric form.

Now, convert the function parametric form.

Substitute $x=r\cos t$ and $y=r\sin t$ .

  $\begin{array}{c}f\left(r,t\right)={\left(r\cos t\right)}^2+{\left(r\sin t\right)}^2\\ =r^2{\cos }^{2}t+r^2{\sin }^{2}t\\ =r^2\left({\cos }^{2}t+{\sin }^{2}t\right)\\ =r^2\end{array}$

So the obtained function $f\left(r,t\right)$ also drawn but have to use parametric form to draw it.

So, it is not mandatory that the graph of a function always be given parametric form.

Therefore, the given statement is not true and depends on the function.