From cb1ce4e53abf2b37cfeec210603ff7db341e2a32 Mon Sep 17 00:00:00 2001
From: eggy <danielchen04@hotmail.ca>
Date: Tue, 10 Jan 2023 16:04:33 -0500
Subject: [PATCH] math119: fail sketching variables

---
 docs/1b/math119.md | 11 +++++++++++
 1 file changed, 11 insertions(+)

diff --git a/docs/1b/math119.md b/docs/1b/math119.md
index 2fe0f49..4a959d8 100644
--- a/docs/1b/math119.md
+++ b/docs/1b/math119.md
@@ -23,3 +23,14 @@ $$f: \mathbb R^n \to \mathbb R$$
 
 Please see [level set](https://en.wikipedia.org/wiki/Level_set) and [contour line](https://en.wikipedia.org/wiki/Contour_line) for example images.
 
+In order to create a sketch for a multivariable function, this site does not have enough pictures so you should watch a YouTube video.
+
+!!! example
+    For the function $z=x^2+y^2$:
+    
+    For each $x, y, z$:
+    
+    - Set $k$ equal to the variable and substitute it into the equation
+    - Sketch a two-dimensional graph with constant values of $k$ (e.g., $k=-2, -1, 0, 1, 2$) using the other two variables as axes
+    
+    Combine the three **contour plots** in a three-dimensional plane to form the full sketch.