Why do I get two more points on the scaling and wavelet functions when the command WAVEFUN in Wavelet Toolbox is used?

I tried to obtain my scaling and wavelet functions by typing the command:

[phi,psi,xval] = wavefun('haar',4)

at the MATLAB command prompt.

Using the command above, my results always have 18 points instead of 2^4 or 16 points that I have expected.

 phi =

   Columns 1 through 10 

          0    1.0000    1.0000    1.0000    1.0000    1.0000    1.0000    1.0000    1.0000    1.0000

   Columns 11 through 18 

     1.0000    1.0000    1.0000    1.0000    1.0000    1.0000    1.0000         0

 psi =

   Columns 1 through 10 

          0    1.0000    1.0000    1.0000    1.0000    1.0000    1.0000    1.0000    1.0000   -1.0000

   Columns 11 through 18 

    -1.0000   -1.0000   -1.0000   -1.0000   -1.0000   -1.0000   -1.0000         0

 xval =

   Columns 1 through 10 

          0    0.0625    0.1250    0.1875    0.2500    0.3125    0.3750    0.4375    0.5000    0.5625

   Columns 11 through 18 

     0.6250    0.6875    0.7500    0.8125    0.8750    0.9375    1.0000    1.0625

Answer 1

[MathWorks Support Team]

The two points, one at the beginning and one at the end, are added solely for plotting purposes. Without adding the two points for plotting, the plotted function will not be correct. The two added points are outside the function interval. The function itself still has the correct number of points.