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:

$\begin{gathered} y_{max}=5 \\ y_{min}=-4 \end{gathered}$