Complete the below problem and on a separate document complete the attached quiz showing all work for both.

Theorem 1.7. Transformations. Suppose f is a function. If A 6= 0 and B 6= 0, then to graph g(x) = Af(Bx + H) + K 1. Subtract H from each of the x-coordinates of the points on the graph of f. This results in a horizontal shift to the left if H > 0 or right if H < 0. 2. Divide the x-coordinates of the points on the graph obtained in Step 1 by B. This results in a horizontal scaling, but may also include a reflection about the y-axis if B < 0. 3. Multiply the y-coordinates of the points on the graph obtained in Step 2 by A. This results in a vertical scaling, but may also include a reflection about the x-axis if A < 0. 4. Add K to each of the y-coordinates of the points on the graph obtained in Step 3. This results in a vertical shift up if K > 0 or down if K < 0.

Suppose (2, −3) is on the graph of y = f(x). In Exercises 1 – 18, use Theorem 1.7 to find a point on the graph of the given transformed function.

* Use some additional/different points for the problem

14. y = 5f(2x + 1) + 3

Quiz 2 – SUMMER 2020 – MATH 107 6387 – COLLEGE ALGEBRA

University of Maryland Global Campus

SUMMER 2020, MATH 107 6387

Quiz 2

Prof.

Minhtri Ho

Quiz 2 has 10 problems with each problem being worth 10 points.

The total score of Quiz 2 is 100 points and it counts for 10 % of the final grade of the class.

Please submit Quiz 2 by 11:59 PM Eastern Time June 9, 2020.

Problem 1:

Express the following sets of numbers using interval notation:

{x|x ≤ −2 or x ≥ 0}

Problem 2:

Find the midpoint of the line segment connecting P (−2; 5) and Q(4; −3)

Problem 3:

Determined whether or not (−1, 0) is on the graph x2 + y 3 = 1.

Problem 4:

Find the x− and y− intercepts (if any) of the graph of (x − 2)2 + y 2 = 25.

SUMMER 2020 – MATH 107 6387 – COLLEGE ALGEBRA

Quiz 2 – SUMMER 2020 – MATH 107 6387 – COLLEGE ALGEBRA

Problem 5:

Use the Vertical Line Test to determine if the following relation describes y as a function

of x.

Problem 6:

What are the domain and range of the following function:

f (x) =

√

x3 − 8

Problem 7:

What are the domain and range of the following function:

f (x) =

√

7−x

SUMMER 2020 – MATH 107 6387 – COLLEGE ALGEBRA

Quiz 2 – SUMMER 2020 – MATH 107 6387 – COLLEGE ALGEBRA

Problem 8:

The area A enclosed by a square, in square inches, is a function of the length of one of its

sides x, when measured in inches. This relation is expressed by the formula A(x) = x2 for

x > 0. Find A(2) and solve A(x) = 49. Interpret your answers to each. Why is x restricted

to x > 0?

Problem 9:

Let f (x) = 6×2 − x and g(x) = 4 − x1 . Find (f + g)(−1)

Problem 10:

Find and simplify the difference quotient for the following function:

f (x) = x2 − 2x + 3

SUMMER 2020 – MATH 107 6387 – COLLEGE ALGEBRA