Question

these functions are called
the parent function is y =
the domain is:
the range is:
this function has been shifted
this function has been reflected over
this function has been.... (circle one each below, if applicable)
stretched/compressed
vertically/horizontally

these functions are called
the parent function is y =
the domain is:
the range is:
this function has been shifted
this function has been reflected over
this function has been.... (circle one each below, if applicable)
stretched/compressed
vertically/horizontally

Explanation:

Step1: Analyze left - hand side graph

The left - hand side graph is a square root - type function. The general form of a square - root function is $y = a\sqrt{b(x - h)}+k$. The parent function of square - root functions is $y=\sqrt{x}$. The domain of $y = \sqrt{x}$ is $x\geq0$. For the given graph, the domain is $x\geq0$. The range of the parent function $y=\sqrt{x}$ is $y\geq0$, and for the given graph, the range is $y\leq - 1$. It has been reflected over the $x$ - axis (because the graph opens downwards instead of upwards like the parent function $y = \sqrt{x}$), shifted down 1 unit. There is no stretching or compressing indicated.

Step2: Analyze right - hand side graph

The right - hand side graph is a linear function. The general form of a linear function is $y=mx + b$. The parent function of linear functions is $y = x$. The domain of a linear function $y=mx + b$ is all real numbers, i.e., $(-\infty,\infty)$. The range is also all real numbers, $(-\infty,\infty)$. It has a $y$ - intercept of 2 and a positive slope, so it has been shifted up 2 units from the parent function $y = x$ and has not been reflected, stretched or compressed in a non - trivial way.

Answer:

Left - hand side graph:
These functions are called square - root functions.
The parent function is $y=\sqrt{x}$.
The domain is: $x\geq0$.
The range is: $y\leq - 1$.
This function has been shifted down 1 unit.
This function has been reflected over the $x$ - axis.
This function has not been stretched/compressed.

Right - hand side graph:
These functions are called linear functions.
The parent function is $y = x$.
The domain is: $(-\infty,\infty)$.
The range is: $(-\infty,\infty)$.
This function has been shifted up 2 units.
This function has not been reflected.
This function has not been stretched/compressed.