During this challenge we were asked to use desmos and our knowledge of functions and relations to create a Santa face. We were also required to include domain, range and different colors in the graph. Below I will attempt to explain in detail the relations/functions I used and the skills I developed during the completion of this assignment.

Here is the brief summary and explanation of the various functions and relations that I used:

1. Absolute Value Function: The general form of an absolute value function is f(x)=a|x – h|+ k, where a,h and k are real numbers with the vertex at (h,k). H controls the horizontal translation, K controls the vertical translation and A determines the direction the graph opens.
2. Equation of a Circle: In its simplest form is (x-h)²+(y-k)²=r² with the center being at the point (h,k) and the radius being “r”. This form is very useful because it allows us to easily find the center and the radius of the circle. However, they are also often given in the form of ax² +by² +cx +dy+ e=0
3. Linear Functions: Linear functions essentially allow us to graph straight lines on the coordinate plane. It is commonly written in the slope-intercept form: y=mx+b, where m is the slope and b is the y-intercept of the line.
4. Quadratic Functions: A quadratic function is a second degree polynomial function. The graph is called a parabola. The vertex form of a quadratic function is f(x)=a(x-h)²+k, where (h,k) is the vertex of the parabola. The H represents the horizontal shift, K shows the vertical shift and A determines the direction the graph opens up.
   

In conclusion, I found this assignment very interesting and challenging. I used estimations, inequalities, constants, domain/range and reciprocals to create this graph. During the process I was required to use a variety of techniques and problem solving strategies which resulted in a significant improvement of my skills and knowledge in this unit.