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Chapter 9: Q. 11. (page 755)

Explain how to use parametric equations to transform the

function y=f(x)

Short Answer

Expert verified

The parametric equations arex=t,y=f(t)

Step by step solution

01

Given information

The function is y=f(x)where yis 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.

02

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

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

Hence, the parametric equations are

x=t,y=f(t)

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Most popular questions from this chapter

Each of the integrals or integral expressions in Exercises 38-44represents the area of a region in the plane. Use polar coordinates to sketch the region and evaluate the expressions.

Use Cartesian coordinates to express the equations for the parabolas determined by the conditions specified in Exercises 22鈥�31.

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In Exercises 24鈥�31 find all polar coordinate representations for the point given in rectangular coordinates.

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Use Cartesian coordinates to express the equations for the parabolas determined by the conditions specified in Exercises 22鈥�31.

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In Exercises 24鈥�31 find all polar coordinate representations for the point given in rectangular coordinates.

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