zMath 180  - Unit 22: Relations and Functions
1) Use the table below to determine the corresponding “y” values for the given “x” values for the function, y = 2x – 5. When x = 1, the function rule is y = 2(1) – 5 and the output is y = –3. State the rule, and then the value for “y” when x = 2, 3, 4, and 5.

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2) In the previous problem, when x = 1, the ordered pair for the function, y = 2x – 5 is (1, –3). What are the four ordered pairs for x = 2, 3, 4, and 5?

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3) On graph paper, graph the points listed in the previous problem. Connect the points. Describe the figure.

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4) Why is the following set of ordered pairs considered a relation and NOT a function?

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5) Given the ordered pairs shown below, what must be done to the x-coordinate to obtain the corresponding y-coordinate?

6) For the function shown below, look at the y-values of the ordered pairs. In words, describe how to determine the y-coordinate given the x-coordinate?

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7) For the function in the previous problem, which algebraic expression fits the function?

8) For the function referenced in the previous two problems, predict three more ordered pairs for the function.

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9) In the table shown below, the same rule is used to match each number in the X-row with a number in the Y-row. The table is torn and part of it is missing. What number should replace the question mark above 53?

10) In the previous problem, what equation represents the rule for the function?

Review

11) What is the volume of a square prism with a base area of 25 square centimeters and a height of 6 centimeters?

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12) What is the volume of a cylinder that has a base area of 16.5 square centimeters and the height is 11 centimeters? Express the answer in tenths.

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13) What is the volume of a cylinder if the radius is 3.2 centimeters and the height is 5 centimeters? Express the answer in thousandths.

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14) What is the surface area of a cylinder with a radius of 3.1 centimeters and a height of 10 centimeters? Express the answer in hundredths.

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15) What is the surface area of a cylinder with a radius of 4 centimeters and a height of 5 centimeters? Express the answer in hundredths.

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16) What is the surface area of a rectangular prism that measures 3 centimeters by 5 centimeters by 7 centimeters?

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17) What is the volume of a rectangular prism that measures 3 centimeters by 4 centimeters by 5 centimeters?

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18) Given the surface area of a cube is 600 square centimeters, what is the length of one edge of the cube? Label the answer correctly.

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19) What is the volume of the cube mentioned in the previous problem? Label the answer correctly.

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20) What is the surface area of a regular triangular prism with the following dimensions: the base edge of the equilateral triangle is 3.5 centimeters and the height of the base triangle is 3 centimeters, the length of the prism is 4 centimeters?

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21) What is the surface area of a square pyramid with a square base of 4 centimeters by 4 centimeters and a slant height of 6 centimeters?

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22) What is the volume of a square pyramid with a base of 4 centimeters by 4 centimeters and a height of 5 centimeters? Express the answer in hundredths.

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For the next two problems, refer to the following description of the triangular pyramid. The base edges are a triangle that measures 3 centimeters by 3 centimeters by 5 centimeters. The height of the base triangle is 1.6 centimeters. This height is drawn to the 5-centimeter edge. The height of the pyramid is 4 centimeters.

23) What is the volume of the triangular pyramid? Express the answer in hundredths. Note: Not all measurements given in the description will be used to calculate the volume. (Hint: V = (1/3) B h)

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24) What is the surface area of the pyramid if the slant heights of the side triangles are 4.2 centimeters, 4.2 centimeters, and 4.8 centimeters? (Hint: One measurement given in the original description will not be used when calculating the surface area.)

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25) Explain how to find the height of a pyramid if the base area and the volume is known. (Hint: Work backwards.)

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On graph paper, draw trapezoid ABCD with vertices A(–4,1), B(–2,4), C(1,4), and D(3,1) on a coordinate plane (with x-y axis). Draw the trapezoid three times in three different coordinate planes. For each of the next three problems, transform the trapezoid as directed to form a new image, and then list the ordered pairs of the image. (When starting each transformation, refer back to the original ordered pairs given, and then perform the action.)

26) Translate the trapezoid left 3 units. List the ordered pairs of the image.

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27) Translate the trapezoid down 7 units. List the ordered pairs of the image

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28) Reflect the trapezoid over the x-axis. List the ordered pairs of the image.

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Draw a sketch of similarity based on the facts given, and then solve the next four problems. (Note: Draw the triangles so that vertex X corresponds to vertex R, vertex Y corresponds to vertex S, and vertex Z corresponds to vertex T.)

29) What is true about each of the corresponding angles of the similar triangles?

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30) ST = ?

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31) TR = ?

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32) What is the common ratio between the proportional sides of the similar triangles?

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33) Evaluate.

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34) Evaluate.

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35) What is cost to carpet a hallway measuring 10 FEET by 3 FEET at $33 per SQUARE YARD?

36) Courtney solved the inequality, x + 6 > –2, and graphed the solution as shown below. What is wrong with Courtney’s graph?

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37) Solve for “x” using inverse operations.

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