Question

How can I access graph package for illustrating solutions to questions?

Answer 1

Click on the 'Graph' button in the toolbar, then enter the equation of function you wish to graph.

Explanation:

When answering a question, the toolbar above the edit window contains a 'Graph' button.

Clicking this button will bring up a window in which to enter the formula of the function to graph.

You can express the formula as a function of `x`, or write an equation in terms of `x` and `y`.

If you want to graph more than one function at once express the formula as the product of terms equated to zero, i.e. in the form `(y - f(x))(y - g(x)) = 0`, etc.

graph{((x+3)^100+(y-3)^100-2^100)((x-3)^100+(y-3)^100-2^100)(x^2+(y-3)^2-7)(y-3-sin(x)) = 0 [-9.96, 10.04, -2.48, 7.52]}

To limit the graph to a particular horizontal interval `[a,b]`, you can multiply by an expression of the form `sqrt((x-a)(b-x))`.

For example, here I multiply by `sqrt(9-x^2)` to limit the horizontal interval to `[-3, 3]` ...

graph{sqrt(9-x^2)((x+3)^100+(y-3)^100-2^100)((x-3)^100+(y-3)^100-2^100)(x^2+(y-3)^2-7)(y-3-sin(x)) = 0 [-9.96, 10.04, -2.48, 7.52]}

To mark individual points you can use small circles, but they can easily disappear or be slightly misdrawn if you make them too small.

graph{((x-3)^2+(y-5)^2-0.023)((x+3)^100+(y-3)^100-2^100)((x-3)^100+(y-3)^100-2^100)(x^2+(y-3)^2-7)(y-3-sin(x)) = 0 [-9.96, 10.04, -2.48, 7.52]}

It is possible to get the graphing facility to draw triangles, squares and circles. I have not worked out how to do pentagons yet.

For example:

`((sqrt(3)/2(x-2)/(1-1/sqrt(3)(y-1)))^100+(y-sqrt(3)/2-1)^100-(sqrt(3)/2)^100)((x-4.5)^100+(y-2)^100-1^100)((x-7)^2+(y-2)^2-1^2) = 0`

graph{((sqrt(3)/2(x-2)/(1-1/sqrt(3)(y-1)))^100+(y-sqrt(3)/2-1)^100-(sqrt(3)/2)^100)((x-4.5)^100+(y-2)^100-1^100)((x-7)^2+(y-2)^2-1^2) = 0 [-0.2, 9.8, -1.11, 3.89]}