We are given a graph and we are asked to determine the type of function.
We notice that the graph is a line, therefore, it must be of the form:
[tex]y=mx+b[/tex]
Where "m" is the slope and "b" is the y-intercept.
The y-intercept "b" is the point where the line crosses the y-axis since from the graph we notice that the line crosses the y-axis at y = 0, we have:
[tex]\begin{gathered} y=mx+0 \\ y=mx \end{gathered}[/tex]
Also, we notice that the point:
[tex](x,y)=(1,1)[/tex]
Is part of the line, therefore, we can substitute in the equation and we get:
[tex]\begin{gathered} 1=m(1) \\ 1=m \end{gathered}[/tex]
Therefore, the slope is 1. Substituting we get:
[tex]y=x[/tex]
Therefore, the right answer is identity y = x.
