8.7.7  Intersection of a 2D graph with the axis

You can find the intersection of the graph y=f(x) of a function with the axes using the commands covered so far.

• Finding the intersection of the graph with the y-axis is simply evaluating

  f(0),

  indeed the point with coordinates (0,f(0)) is the intersection point of the graph of f with the y-axis.
• Finding the intersection of the graph of f with the x-axis requires solving the equation f(x)=0.
  • If f(x) is polynomial-like, then you can find the the exact values of the abscissa of these points with solve (see Section 6.55.6).
    Input:
    solve(f(x),x)
    returns the solution.
  • Otherwise, you can find numeric approximations of these abscissa. First, look at the graph for an initial guess x₀ or a range with an intersection and then refine it with fsolve (see Section 10.4).
    Input:
    fsolve(f(x),x,x₀,method)
    returns a numeric approximation of a solution.