Question

MATLAB!

Evaluate the function y=(x-(1/x))/(1+(1/x^2)) for x varying from -2 to 2 with 0.01 steps. Plot the function (y versus x) as a line such that it's blue when y<-0.2, red when y<0.2, and green for all the other values.

Answer 1

% Matlab script to plot the function (y versus x) as a line such that it's blue when y<-0.2, red when y<0.2, and green for all the other values.

% define the x vector
x = (-2:0.01:2);
% calculate the y vector
y=(x-(1./x))./(1+(1./x.^2));

% use find function to get the indexes for y < -0.2 , y >= -0.2 and y < 0.2
% and y >= 0.2
idx1 = find(y < -0.2);
idx2 = find( y >= -0.2 & y < 0.2);
idx3 = find(y>=0.2);

% create a new vectors for x and y to contain all the points to be shown
% with blue line, red line and green line respectively
xBlue = x;
yBlue = y;
xRed = x;
yRed = y;
xGreen = x;
yGreen = y;

% set the points in xBlue which belong to red or green line to NaN so that
% it is not plotted
xBlue(idx3) = NaN;
xBlue(idx2) = NaN;
yBlue(idx3) = NaN;
yBlue(idx2) = NaN;

% Similarly, set the points in xRed which belong to blue or green line to NaN so that
% it is not plotted
xRed(idx3) = NaN;
xRed(idx1) = NaN;
yRed(idx3) = NaN;
yRed(idx1) = NaN;

% Similarly, set the points in xGreen which belong to red or bue line to NaN so that
% it is not plotted
xGreen(idx1) = NaN;
xGreen(idx2) = NaN;
yGreen(idx1) = NaN;
yGreen(idx2) = NaN;

% plot the blue line
plot(xBlue,yBlue,'b-');
hold on; % hold the current graph so that subsequent plot are plotted in the same graph
% plot the red line
plot(xRed,yRed,'r-');
% plot the green line
plot(xGreen,yGreen,'g-');
hold off; % release the current graph
xlabel('X');
ylabel('Y');
% end of script

Output: