How to plot a function ?

Helli, i'm a newbie in mathlab and i try for hours to make the program below, please would you explained me how to begin or make the program and write the code to see where i make some mistake.

Write a program that recieve as arguments two real numbers a and b with a>0 and b∈(0,1) and who represent graphic in cartesian coordinate function f:[0,2]->R.

       { (a*x)/(x^2+b), x∈[0,1]
f(x)=  {
       { ln(x^2-3*x+3), x∈(1,2]

with dashed line and black color. The program display an error message if the requirements about arguments are not respected.

Thank You!!

Answer 1

[Carlos]

Some ideas here

function y=new(a,b)
if(a<0)
  disp('a must be bigger than zero');
end
if(b<0||b>1)
  disp('a must be bigger than zero and smaller than 1');
end
x=0:0.1:2;
y=zeros(1,length(x));
for k=1:length(x)
  if (x(k)<1)
  y(k)=(a*x(k))/(x(k)^2+b);
  else
  y(k)=log(x(k)^2-3*x(k)+3);
  end
end
plot(x,y)

[Niklas Nylén]

The if statement is incorrect since it treats x as a scalar and not as a vector.

[Carlos]

My bad, you are right.

[Alexandru Stefan]

Thank you, both were really helpful.

Answer 2

[Niklas Nylén]

 function fx = myFunction(a,b)
 x=0:0.1:2; % Create the x vector with step size 0.1
 fx = zeros(size(x)); % Initialize the function output fx with zeros

 % Make the calculation for when x<=1
 index = x <= 1; % Creates a logical vector with 0's and 1's
 % Calculate f(x) for the indices of x which fulfill the previous logical statement
 fx(index) = (a.*x(index))./(x(index).^2+b); 

 % Use the second equation when x > 1
 index = x > 1;
 fx(index) = log(x(index).^2-3.*x(index)+3);

 figure; 
 plot(x,fx)

[Alexandru Stefan]

Thank You was really helpful, one more question how to make the program show an error if the requirements about arguments are not respected.

[Carlos]

I have edited my previous code including the imput argument control you requested