Function Repository Resource:

Intercepts (9.0.0) current version: 10.0.0 »

Source Notebook

Compute the intercepts of a function with the coordinate axes

Contributed by: Wolfram|Alpha Math Team

ResourceFunction["Intercepts"][expr,{x,y,…}]

finds the intercepts of the expression expr with respect to the axis variables x,y,….

ResourceFunction["Intercepts"][expr,var,x]

returns only the x-intercepts of the graph of expr.

Details and Options

The first argument expr should be an equation (having head Equal).

ResourceFunction["Intercepts"] accepts the option "Constraints", expecting a logical combination of equalities and inequalities involving the axis variables.

Results of ResourceFunction["Intercepts"][expr,{x,y},…] are returned in an association of the form <|x→{{x₁,0},{x₂,0}…},y→…|>.

Examples

Basic Examples (3)

Find the intercepts of a line:

In[1]:=

Out[1]=

In[2]:=

Out[2]=

Find the intercepts of a parabola:

In[3]:=

$ResourceFunction["Intercepts"][y == x^2 + 2 x - 3, {x, y}]$

Out[3]=

In[4]:=

$Plot[x^2 + 2 x - 3, {x, -4, 2.5}, Epilog -> Join[{Red, PointSize@Large}, Point /@ Flatten[Values[%], {1}]] ]$

Out[4]=

Find the intercepts of an implicitly-defined circle:

In[5]:=

$ResourceFunction["Intercepts", ResourceVersion->"9.0.0"][(x - 1.75)^2 + (y - 0.3)^2 == 9, {x, y}]$

Out[5]=

In[6]:=

$Plot[{0.3 + Sqrt[9 - (x - 1.75)^2], 0.3 - Sqrt[9 - (x - 1.75)^2]}, {x, -5, 5}, Epilog -> Join[{Red, PointSize@Large}, Point /@ Flatten[Values[%], {1}]] ]$