Graphing Parametric Equations with Non-Linear Constraints

In summary, the conversation discusses how to graph the equations x = t and y = 2t, and the confusion surrounding the condition y ≠ f(x). It is noted that the definitions of x and y imply y = 2x, which is easily graphed. However, the statement y ≠ f(x) may not make sense as no function has been given for y in terms of x. It is suggested that in this case, f(x) = 2x would fulfill this condition. The conversation also briefly touches on the possibility of y ≠ t, but it is uncertain what this assertion means.
  • #1
mymachine
42
0
If x = t, y = 2t, and y ≠ f(x), how to graph these equations?
 
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  • #2
Plot a point for every t.
Alternatively, calculate y=f(x).
 
  • #3
Your condition y ≠ f(x) doesn't make sense. The definitions you give for x and y imply y = 2x, which is easily graphed.
 
  • #4
mathman said:
Your condition y ≠ f(x) doesn't make sense. The definitions you give for x and y imply y = 2x, which is easily graphed.

In this case, y is ≠ f(x).
 
  • #5
mymachine said:
In this case, y is ≠ f(x).

Possibly what you mean to say is that no function has been given for y in terms of x.

In some cases it is true that no function exists for y in terms of x. This would be because there are some values of x that pair up with more than one value for y. However, in the case at hand, it is trivial to find an f() such that y = f(x).
 
  • #6
mymachine said:
In this case, y is ≠ f(x).

f(x) = 2x. What does your assertion mean?
 
  • #7
Maybe he meant for y ≠ t?
 

1. What are parametric equations?

Parametric equations are a set of equations that express the coordinates of a point in terms of one or more independent variables, known as parameters. These equations are commonly used in mathematics and physics to describe curves and surfaces.

2. How do parametric equations differ from cartesian equations?

Cartesian equations are written in terms of x and y coordinates, while parametric equations are written in terms of parameters. This means that parametric equations can describe more complex shapes and curves, as they are not limited to a single equation.

3. What is the purpose of using parametric equations?

Parametric equations are used to describe curves and surfaces that cannot be easily expressed using cartesian equations. They also allow for more flexibility and control in manipulating and graphing these shapes.

4. How do you graph parametric equations?

To graph parametric equations, you can plot points by substituting different values for the parameters and then connecting the points. You can also use a graphing calculator or computer software to graph parametric equations.

5. What are some real-world applications of parametric equations?

Parametric equations are used in a variety of fields, such as engineering, physics, and computer graphics. They can be used to model the motion of objects, design curves and surfaces, and create 3D animations.

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