Plotting piece-wise functions with absolute value????

Hi, I want to plot this piece-wise function:

f(x) = { x if -5<=x<=5 x^2 if x<-5 or x>5

I started out how I've plotted piece-wise functions in the past, with a for-loop and if statemnts

   x = linspace (-10,10,100)

   for k = 1: length(x)

     if (x(k) >= -5 & x(k)<=5)
        y(k) = abs(x)

     elseif (x(k)<-5 | x(k)>2)
            y(k) = x.^2
end
end
plot (x,y)

I keep getting this error:

In an assignment A(I) = B, the number of elements in B and I must be the same.

Error in piecewise (line 6) y(k) = x.^2;

I cannot figure out how to plot this particular equation. Please help?

Answer 1

[Youssef Khmou]

The algorithm you wrote is almost correct, inside the if conditions you need to use x(k), not x :

x = linspace (-10,10,100);
 for k = 1: length(x)
   if (x(k) >= -5 && x(k)<=5)
      y(k) = abs(x(k));
   elseif (x(k)<-5 || x(k)>2)
          y(k) = x(k).^2;
end
end
plot (x,y)

There are other methods to generate piece wise functions.

Answer 2

[David Young]

To fix your existing code, with the loop, you need

y(k) = abs(x(k));

and

y(k) = x(k).^2;

Your condition x(k) > 2 in the elseif line looks wrong - it isn't what you say you want to do at the start, and it isn't consistent with the else condition. Assuming it should be x(k) > 5, you should simply replace the whole elseif line with "else".

Alternatively, you can just use MATLAB's vectorisation capability to avoid the loop altogether. Replace the loop with:

middlePart = x >= -5 & x <= 5;
y(middlePart) = abs(x(middlePart));
y(~middlePart) = x(~middlePart) .^ 2;

Note the difference between this and the looping version. With the loop, you operate on x(k), which is a scalar. With the vectorised version you operate on vectors.