# 11.9: Chapter 11 Review

Difficulty Level: At Grade Created by: CK-12

Explain the shift of each function from the parent function \begin{align*}f(x)=\sqrt{x}\end{align*}.

1. \begin{align*}f(x)=\sqrt{x}+7\end{align*}
2. \begin{align*}f(x)=\sqrt{x+3}\end{align*}
3. \begin{align*}g(x)=-\sqrt{x}\end{align*}
4. \begin{align*}y=3+\sqrt{x-1}\end{align*}

Graph the following square root functions. Identify the domain and range of each.

1. \begin{align*}f(x)=\sqrt{x-2}+5\end{align*}
2. \begin{align*}g(x)=-\sqrt{x+1}\end{align*}
3. \begin{align*}f(x)=\sqrt{2x}-2\end{align*}

Simplify the following, if possible. Write your answer in its simplest form.

1. \begin{align*}\sqrt{\frac{3}{7}} \times \sqrt{\frac{14}{27}}\end{align*}
2. \begin{align*}\sqrt{5} \cdot \sqrt{7}\end{align*}
3. \begin{align*}\sqrt{11} \times \sqrt[3]{11}\end{align*}
4. \begin{align*}\frac{\sqrt{18}}{\sqrt{2}}\end{align*}
5. \begin{align*}8\sqrt[3]{4}+11\sqrt[3]{4}\end{align*}
6. \begin{align*}5\sqrt{80}-12\sqrt{5}\end{align*}
7. \begin{align*}\sqrt{10}+\sqrt{2}\end{align*}
8. \begin{align*}\sqrt{24}-\sqrt{6}\end{align*}
9. \begin{align*}\sqrt[3]{27}+\sqrt[4]{81}\end{align*}
10. \begin{align*}4\sqrt{3} \cdot 2\sqrt{6}\end{align*}
11. \begin{align*}\sqrt[3]{3} \times \sqrt{7}\end{align*}
12. \begin{align*}6\sqrt{72}\end{align*}
13. \begin{align*}7\sqrt{\left (\frac{40}{49} \right )}\end{align*}
14. \begin{align*}\frac{5}{\sqrt{75}}\end{align*}
15. \begin{align*}\frac{\sqrt{45}}{\sqrt{5}}\end{align*}
16. \begin{align*}\frac{3}{\sqrt[3]{3}}\end{align*}
17. \begin{align*}8\sqrt{10}-3\sqrt{40}\end{align*}
18. \begin{align*}\sqrt{27}+\sqrt{3}\end{align*}

Solve each equation. If the answer is extraneous, say so.

1. \begin{align*}8=\sqrt[3]{2k}\end{align*}
2. \begin{align*}x=\sqrt{7x}\end{align*}
3. \begin{align*}\sqrt{2+2m}=\sqrt{4-m}\end{align*}
4. \begin{align*}\sqrt[4]{35-2x}=-1\end{align*}
5. \begin{align*}14=6+\sqrt{10-6x}\end{align*}
6. \begin{align*}4+\sqrt{\frac{n}{3}}=5\end{align*}
7. \begin{align*}\sqrt{-9-2x}=\sqrt{-1-x}\end{align*}
8. \begin{align*}-2=\sqrt[3]{t-6}\end{align*}
9. \begin{align*}5\sqrt{10}=6\sqrt{w}\end{align*}
10. \begin{align*}\sqrt{x^2+3x}=2\end{align*}
11. \begin{align*}\sqrt[4]{t}=5\end{align*}
12. A leg of a right triangle is 11. Its hypotenuse is 32. What is the length of the other leg?
13. Can 9, 12, 15 be sides of a right triangle?
14. Two legs of a right triangle have lengths of 16 and 24. What is the length of the hypotenuse?
15. Can 20, 21, and 29 be the sides of a right triangle?

Find the distance between the two points. Then find the midpoint.

1. (0, 2) and (–5, 4)
2. (7, –3) and (4, –3)
3. (4, 6) and (–3, 0)
4. (8, –3) and (–7, –6)
5. (–8, –7) and (6, 5)
6. (–6, 6) and (0, 8)
7. (2, 6) is six units away from a second point. Find the two possibilities for this ordered pair.
8. (9, 0) is five units away from a second point. Find the two possibilities for this ordered pair.
9. The midpoint of a segment is (7.5, 1.5). Point \begin{align*}A\end{align*} is (–5, –6). Find the other endpoint of the segment.
10. Maggie started at the center of town and drove nine miles west and five miles north. From this location, she drove 16 miles east and 12 miles south. What is the distance from this position from the center of town? What is the midpoint?
11. The surface area of a cube is given by the formula \begin{align*}SA=6s^2\end{align*}. The surface area is 337.50 square inches. What is the side length of the cube?
12. The diagonal of a sail is 24 feet long. The vertical length is 16 feet. If the area is found by \begin{align*}\frac{1}{2} (length)(height)\end{align*}, determine the area of the sail.
13. A student earned the following test scores: 63, 65, 80, 84, 73. What would the next test score have to be in order to have an average of 70?
14. Find the mean, median, mode, and range of the data set. 11, 12, 11, 11, 11, 13, 13, 12, 12, 11, 12, 13, 13, 12, 13, 11, 12, 12, 13
15. A study shows the average teacher earns $45,000 annually. Most teachers do not earn close to this amount. 1. Which central tendency was most likely used to describe this situation? 2. Which measure of central tendency should be used to describe this situation? 16. Mrs. Kramer’s Algebra I class took a test on factoring. She recorded the scores as follows: 55, 57, 62, 64, 66, 68, 68, 68, 69, 72, 75, 77, 78, 79, 79, 82, 83, 85, 88, 90, 90, 90, 90, 92, 94, 95, 97, 99 1. Construct a histogram using intervals of ten, starting with 50–59. 2. What is the mode? What can you conclude from this graph? 17. Ten waitresses counted their tip money and collected the following data:$32, $58,$17, $27,$69, $73,$42, $38,$24, and \$52. Display this information in a stem-and-leaf plot.
18. Eleven people were asked how many miles they live from their place of work. Their responses are: 5.2, 18.7, 8.7, 9.1, 2.3, 2.3, 5.4, 22.8, 15.2, 7.8, 9.9. Display this data as a box-and-whisker plot.
19. What is one disadvantage to a box-and-whisker plot?
20. Fifteen students were randomly selected and asked, “How many times have you checked Facebook today?” Their responses are: 4, 23, 62, 15, 18, 11, 13, 2, 8, 7, 12, 9, 14, 12, 20. Display this information as a box-and-whisker plot and interpret its results.
21. What effect does an outlier have on the look of a box-and-whisker plot?
22. Multiple Choice. The median always represents which of the following? A. The upper quartile B. The lower quartile C. The mean of the data D. The 50% percentile

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