MATH 107 University of Maryland University College Algebra Quiz Questions

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