0. Review of College Algebra

Suppose point D has coordinates $(x,y)$. After a translation by $(3,-2)$, what is the new y-coordinate of point D?

Given segment $BC$ in the plane, what is the image of segment $BC$ after a $120$-degree clockwise rotation about point $H$?

Given that one vertex of a polygon is located at $(3,-2)$ and after a rotation it is located at $(2,3)$, what is the angle and direction of the rotation about the origin?

A triangle is rotated $90°$ counterclockwise about the origin. Which rule describes the transformation of a point $(x,y)$?

Which of the following transformations appears to be a translation of the graph of $y=\sin \left(x\right)$?

Given the function $f\left(x\right)$ and its image $g\left(x\right)$ where $g\left(x\right)=f(x-2)$, which transformation maps the pre-image to the image?

Written below (green dotted curve) is a graph of the function $f\(\left\)(x\(\right\))=\(\sqrt{x-2}\)$.If g(x) (blue solid curve) is a reflection of f(x) about the y-axis what is the equation for g(x)?

Given the point $A(5,2)$, what are the coordinates of $A\text{'}$ after reflecting across the line $x=3$?

The green dotted curve below is a graph of the function $f\(\left\)(x\(\right\))$. Find the domain and range of $g\(\left\)(x\(\right\))$(the blue solid curve), which is a transformation of $f\(\left\)(x\(\right\))$.

The green dotted line in the graph below represents the function $f\(\left\)(x\(\right\))$. The blue solid line represents the function $g\(\left\)(x\(\right\))$, which is the function $f\(\left\)(x\(\right\))$after it has gone through a shift transformation. Find the equation for $g\(\left\)(x\(\right\))$.