Function Repository Resource:

Intercepts

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]:=

$ResourceFunction[ "Intercepts", ResourceSystemBase -> "https://www.wolframcloud.com/obj/resourcesystem/api/1.0"][y == x^2 + 2 x - 3, {x, y}]$

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]:=

$ResourceFunction[ "Intercepts", ResourceSystemBase -> "https://www.wolframcloud.com/obj/resourcesystem/api/1.0"][(x - 1.75)^2 + (y - 0.3)^2 == 9, {x, y}]$

Out[5]=

In[6]:=

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

Out[6]=

Scope (1)

Intercepts[expr,…] can handle the use of symbolic parameters in expr:

In[7]:=

$ResourceFunction[ "Intercepts", ResourceSystemBase -> "https://www.wolframcloud.com/obj/resourcesystem/api/1.0"][x^2 + a y^2 == 9, {x, y}]$

Out[7]=

Options (2)

Use the "Constraints" option to restrict the results returned:

In[8]:=

$ResourceFunction[ "Intercepts", ResourceSystemBase -> "https://www.wolframcloud.com/obj/resourcesystem/api/1.0"][x^2 + y^2 == 1, {x, y}, "Constraints" -> x >= 0]$

Out[8]=

With the default setting "Constraints"→True, all results are included:

In[9]:=

$ResourceFunction[ "Intercepts", ResourceSystemBase -> "https://www.wolframcloud.com/obj/resourcesystem/api/1.0"][x^2 + y^2 == 1, {x, y}]$

Out[9]=

Publisher

Wolfram|Alpha Math Team

Version History

10.0.0 – 23 March 2023
9.0.0 – 20 August 2020
8.0.0 – 24 January 2020
7.0.0 – 06 September 2019
6.0.0 – 12 June 2019
5.0.0 – 11 June 2019
4.0.0 – 11 June 2019
3.0.0 – 11 June 2019
2.0.0 – 11 June 2019
1.0.0 – 01 February 2019

Related Resources

Author Notes

To view the full source code for Intercepts, run the following code:

FileNameJoin[ReplacePart[FileNameSplit[FindFile["ResourceFunctionHelpers`"]], -1 →"Intercepts.wl"]] // SystemOpen

License Information

This work is licensed under a Creative Commons Attribution 4.0 International License

Wolfram Function Repository

Intercepts

Details and Options