Question

What is one parent function on this picture ? And what is the largest y value and what is the smallest y value

Answer 1

From this pic we can conclude it is function composite of the following parent functions:

The face is a circle, the parent function is:

`(x-h)^2+(y-k)^2=r^2`

The same for the eyes, the smile can be described using a parabola of the form:

`y=ax^2+bc+c`

The vertical line of the body can be described as:

`\begin{gathered} y=a \\ a\in R \end{gathered}`

The arms can be described using a cosine function:

`y=cos(x)`

Finally the legs can be describe using linear equations, one of them has a positive slope and the other one has a negative slope:

`\begin{gathered} y=mx+b \\ and \\ y=-mx+b \end{gathered}`

Finally from the graph the largest y value and the smallest y value are:

`\begin{gathered} y_(max)=5 \\ y_(min)=-4 \end{gathered}`