How do you graph this function?

In summary: I suspect that the region of the xy-plane where the graph of k(x, y) will lie will be the intersection of the three planes.In summary, the given function z = min(2x+1, x+y, 2y+1) represents the minimum value among three planes in R3 and its graph will be the intersection of these three planes in the xy-plane. It would be helpful to graph each individual function first to get an idea of where the graph of the given function will lie.
  • #1
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Homework Statement



For a given fixed value, z, how would the level curves of the function below look like? (i.e. the graph of the function in the xy plane, for some given value z.

z = min(2x+1, x+y, 2y+1)




Homework Equations





The Attempt at a Solution



Ive been working on this for awhile, but I can't seem to get it right.

Thanks,
M
 
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  • #2
michonamona said:

Homework Statement



For a given fixed value, z, how would the level curves of the function below look like? (i.e. the graph of the function in the xy plane, for some given value z.

z = min(2x+1, x+y, 2y+1)




Homework Equations





The Attempt at a Solution



Ive been working on this for awhile, but I can't seem to get it right.

Thanks,
M

My take on this is that all three expressions on the right side of your equation above should be considered functions of x and y. The equations z = f(x, y) = 2x + 1, z = g(x, y) = x + y, and z = h(x, y) = 2y + 1 all represent planes in R3.

The function z = k(x, y) = min{f(x, y), g(x, y), h(x, y)} assigns to each point (x, y) in the domain, whatever number is the smallest of the three functions at that point.

Graphing each of the three functions would be a good start, IMO.
 

What is a function?

A function is a mathematical relationship between two variables, where each input has only one corresponding output.

What are the steps to graph a function?

The steps to graph a function are as follows:1. Identify the independent and dependent variables.2. Choose a suitable scale for each axis.3. Plot the points on the graph.4. Connect the points with a smooth line to represent the function.

How do I determine the domain and range of a function?

The domain of a function is the set of all possible input values, while the range is the set of all possible output values. To determine the domain, look at the independent variable and identify all the values it can take. To determine the range, look at the dependent variable and identify all the values it can take as a result of the input values.

What does the slope of a function represent?

The slope of a function represents the rate of change between two points on the graph. It can also be interpreted as the steepness of the graph at a given point.

How do I interpret a graph of a function?

To interpret a graph of a function, look at the shape of the graph and identify key features such as the intercepts, slope, and any points of interest such as maximum or minimum values. You can also analyze the behavior of the graph as the input values change.

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