MATLAB: How to ‘divide’ the x-axis based on y-values

categorizing x-axis

Here's a sample equation plot:
x = linspace(0,100);
y = @(x) log(x);
plot(x,y(x),'-','LineWidth',2);
And I am attaching three pictures which represent what I would like to have. I want to 'divide' and 'categorize' the x-axis based on certain ranges of y values. Is there a way I can accomplish one or all three of the tasks outlined in attached picture?
Thank you

Best Answer

Hi,
There are really many and nice ways to take the desire output...here just one quick solution with some patches
x = linspace(0,100);
y = @(x) log(x);
plot(x,y(x),'--','LineWidth',2);
x_lim = get(gca,'xlim')
y_lim = get(gca,'ylim')
hold on
patch([0 0 exp(3.75) exp(3.75)],[y_lim(1) y_lim(2) y_lim(2) y_lim(1) ],[1 0.5 0.2],'FaceAlpha',0.2)
text(mean([0 exp(3.75)]),mean(y_lim),'y < 3.75','rotation',90,'FontSize',14,'HorizontalAlignment','center')
patch([exp(3.75) exp(3.75) exp(4) exp(4)],[y_lim(1) y_lim(2) y_lim(2) y_lim(1) ],[1 1 0.2],'FaceAlpha',0.2)
text(mean([exp(3.75) exp(4)]),mean(y_lim),'3.75 < y < 4.00','rotation',90,'FontSize',14,'HorizontalAlignment','center')
patch([exp(4) exp(4) x_lim(2) x_lim(2)],[y_lim(1) y_lim(2) y_lim(2) y_lim(1) ],[0.5 1 0.7],'FaceAlpha',0.2)
text(mean([exp(4) x_lim(2)]),mean(y_lim),'y > 4.00','rotation',90,'FontSize',14,'HorizontalAlignment','center')
grid minor
ylabel('ln(x)')
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