Plotting Level Set f(x,t)=2: Struggling to Find Equation

• bizzo342
In summary, the conversation is discussing a function g and a new function f, and the task is to plot the level set of f and classify the resulting surface. However, the input for f is not provided as an equation, but rather as a graph of g. It is determined that the surface will be symmetric in both x and y, but without knowing the specific shape of the graph of g, it is difficult to classify the surface.
bizzo342
I'm having a really hard time with this question...

Consider the function g: [0,infinity) --> R shown in figure 7 (Figure 7 is just a graph of a curve defined as z=g(s), where the horizontal axis is the s-axis) Let f be a new function given by: z = f(x,t) = g((x^2)+(t^2)-1). Plot the level set: f(x,t)=2. Classify the surface f.

My problem is that it doesn't give me an equation to stick the input into, just some graph ...help!

And I don't even have the graph!
$$f(x,y)= g(x^2)+ y^2- 1= 2$$
$$g(x^2)+ y^2= 3$$
If g is linear (if the graph is a straight line), with positive slope, then this is an ellipse; with negative slope, a hyperbola. Whatever g is, we can see that the surface will be symmetric in both x and y. Without having some idea of what the graph of g looks like, I don't think we can say more.

1. What is a level set?

A level set is a mathematical concept used to represent a set of points that have the same value for a given function. In other words, it is a way to visualize the points on a graph where a specific function has a constant value.

2. How do you plot a level set?

To plot a level set, you need to first find the points on the graph where the function has a constant value. This can be done by solving the equation f(x,t) = 2 for different values of x and t. Once you have a set of points, you can plot them on a graph, connecting them to create a continuous line.

3. Why am I struggling to find the equation for plotting a level set?

Plotting a level set can be challenging because it requires a good understanding of the function and its behavior. It is also important to have a solid understanding of mathematical concepts, such as equations and graphs. If you are struggling, it may be helpful to review these concepts or seek assistance from a math tutor or colleague.

4. Are there any tips for finding the equation for plotting a level set?

One tip for finding the equation for plotting a level set is to start by choosing a specific value for t and solving the equation for x. This will give you a set of points that lie on the level set for that particular value of t. Repeat this process for different values of t to get a better understanding of how the level set changes. Additionally, using graphing software can be helpful in visualizing the level set and finding patterns.

5. How can I use level sets in my research or work?

Level sets have various applications in different fields, such as physics, engineering, and computer science. They can be used to visualize and analyze complex functions, determine the behavior of a system over time, or identify regions of interest in a dataset. By understanding how to plot level sets, you can apply this concept to your own research or work to gain valuable insights and make informed decisions.

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