algebra

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Math 103 College Algebra – Pragel Name:_______________________

Dropbo

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Assignment 3 Fall 201

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Solve the following problems on a separate sheet of paper, showing all work to receive full
credit. Submit your solutions to the dropbox by 1pm on Friday October 4

th
. Late dropbox

assignments will not be accepted. You will be required to submit your dropbox assignments in
, , or x format to receive credit.

1.) Solve the following equation for all real and complex solution(s). Simplify each solution

completely. ��� − 6��� + 14��� − 6�� + 45 = 0

2.) Solve the absolute value inequality

3|4� − 2| ≥ 1

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Graph the solution set on a number line and write the solution in interval notation,

circling and labeling each.

3.) On graph paper, clearly graph the piecewise function

���� = �3� − 2 −�� √�
� < −2−2 < � ≤ 1� > 1

Free online graph paper can be found at the website:

http://www.printfreegraphpaper.com/

4.) The graph of � = �� is horizontally shifted 4 units to the right, then reflected over the �-
axis, then vertically stretched (expanded) by a factor of 2, and then finally vertically

shifted up 5 units to obtain the graph of ����. Write the equation of ����.

5.) If

���� = 1� − 2, ���� = √2�, ℎ��� = 3 − �

a. Compute �� − �����
b. Compute �� !���
c. Compute �”����#
d. Compute the domain of �$�!���
e. Compute the domain of �”ℎ���#

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6.) Algebraically compute the inverse function, ℎ%&���, to
ℎ��� = � − 32� + 1

Identify the range of ℎ��� in interval notation.

7.) On the axes below is the function ����. On the same set of axes, graph and clearly label:
a. ��� − 3�
b. ��−��
c. 2����
d. ���� + 5
e. �%&���

−10

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−10

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8.) Suppose that the Perfectly Legitimate Businessman’s Hotel can rent all 250 of their hotel

rooms if they charge $90 per room. For each $2.50 increase in the room price, 5 fewer
rooms are rented. If they wish to maximize their revenue, what price should they charge

per room? You must solve this problem algebraically to receive credit.