0. Review of College Algebra

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?

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

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)?

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 $g\left(x\right)$.

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 $f\left(x\right)$.

Fill in the blank(s) to correctly complete each sentence.

To graph the function ƒ(x) = x² - 3, shift the graph of y = x² down ___ units.

Fill in the blank(s) to correctly complete each sentence.

The graph of ƒ(x) = (x + 4)² is obtained by shifting the graph of y = x² to the ___ 4 units.

Fill in the blank(s) to correctly complete each sentence.

The graph of ƒ(x) = -√x is a reflection of the graph of y = √x across the ___-axis.

Fill in the blank(s) to correctly complete each sentence.

The graph of ƒ(x) = √-x is a reflection of the graph of y = √x across the ___-axis.

Work each matching problem.

Match each equation in Column I with a description of its graph from Column II as it relates to the graph of y = x².

I II

a. y = (x - 7)² A. a translation to the left 7 units

b. y = x² - 7 B. a translation to the right 7 units

c. y = 7x² C. a translation up 7 units

d. y = (x + 7)² D. a translation down 7 units

e. y = x² + 7 E. a vertical stretching by a factor of 7