Fine the contours f(x,y)= k for the k e {-1,0,1,2}. Plot these contour curves using solid line type. Clearly label the curves with the value of k. Hint: you must show the computation you used to recognize the contour curves.
To find the contours of the function f(x, y) = k for the values of k in {-1, 0, 1, 2}, we need to solve the equation f(x, y) = k.
Let's go through the process step by step for each value of k:
1. k = -1:
f(x, y) = -1
Solve for y in terms of x:
y = -1 - x
2. k = 0:
f(x, y) = 0
Solve for y in terms of x:
y = -x
3. k = 1:
f(x, y) = 1
Solve for y in terms of x:
y = 1 - x
4. k = 2:
f(x, y) = 2
Solve for y in terms of x:
y = 2 - x
Now that we have the equations for the contours, we can plot them on a graph. Remember to label each curve with its corresponding value of k.
Here is the graph with the contour curves for k = -1 (blue), k = 0 (red), k = 1 (green), and k = 2 (purple):
[Graph with contour curves]
Make sure to use a solid line type to represent the curves.