0. Review of College Algebra

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.

Graph each function. See Examples 1 and 2. h(x) = |-½ x|

Graph each function. See Examples 1 and 2. ƒ(x) = -3|x|

Given the function $y=\sin (x-2)+3$, what are the values of the vertical shift $k$ and the phase shift $h$?

If the graph of $y=\sin \left(x\right)$ is transformed to $y=3\sin \left(x\right)$, what is the scale factor of the dilation?

Which of the following sets of transformations will map rectangle $ABCD$ onto itself?

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

Given a point $(a,b)$, what are the coordinates of its image after a reflection across the line $y=-x$?

Given triangle $△\mathrm{QRS}$ is mapped onto triangle $△Q^{\text{'}}{R}^{\text{'}}{S}^{\text{'}}$, which type of transformation could map $△\mathrm{QRS}$ to $△Q^{\text{'}}{R}^{\text{'}}{S}^{\text{'}}$?

Triangle PQR was transformed by a reflection over the y-axis. Which of the following describes the effect of this transformation on the coordinates of each vertex?

Which of the following is the correct mapping rule for a $180°$ rotation about the origin in the coordinate plane?

Given triangle $f$ on the coordinate grid, which triangle represents a translation of triangle $f$?

Which function represents the reflection over the x-axis of $f\left(x\right)$?

Point T is at $(-2,5)$. What are the coordinates of point T' after reflecting over the y-axis followed by the x-axis?