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Some of the questions in this unit may be answered by recording an audio file. If you chose to record the answer, click on the Add Recording button and follow the on-screen instructions closely. Once you have completed and attached the recording, enter the word “COMPLETE” in the text box. (Note: If your computer does not have a built-in microphone, a microphone or microphone/headset combination is needed to record audio.)
Relations and Functions
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| 1)
Explain how to determine if a relation is a function. |
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| 2)
Determine and state if the relation is a function; and then state the domain and range. |
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| 3)
Determine and state if the relation is a function; and then state the domain and range. |
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| 4)
State the relation shown in the graph as a set of ordered pairs. |
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| 5)
For the given relation, answer the following questions. (a) What is the domain? (b) What is the range? (c) Is this relation a function? Explain. |
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| 6)
A rubber ball is dropped from a height of 250 feet. After each bounce, the height of the ball is recorded in the table below. On paper, list a set of ordered pairs (number of bounces, height) for each bounce recorded in the chart, and then answer the following question. Is the height of the bounce of the ball a function of the number of bounces? Explain. |
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Graphing Linear Relations |
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| 7)
Print out the table below for the function y = 2x – 3. Fill in the y-values and the ordered pairs, and then graph the function on graph paper. Answer the following questions: (a) What are the five ordered pairs? b) Is the graph of the function, linear (straight line) or nonlinear (curved line)? |
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| 8)
Write three ordered pairs for the points (red circles) on the line. |
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| 9)
Which equation represents the relationship of “x” and “y” in the linear graph? |
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| 10)
Identify the coordinates of the point designated by a diamond and the point designated by the triangle. Which set of coordinates will make a true statement when substituting the x-coordinate in for “x” and the y-coordinate in for “y” in the equation of the linear graph? |
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| 11)
Select the terms that will complete the following sentence: The values of the coordinates of the points that are located on the graph of the line of an equation will test __________ when substituted in the equation; and, the values of the coordinates of all points NOT located on the line will test__________. |
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| 12)
Graph y = 2x – 5. (a) State three ordered pairs for points that will test true in the equation. (b) State one ordered pair for a point that will test false in the equation. |
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For the next two problems, determine if the equations are linear. If the equation is linear, write “yes”. If the equation is NOT linear, write “no” and explain why. |
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Linear? |
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Linear? |
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| 15)
What are the x-intercept and the y-intercept of the linear equation, 4x + 3y = 12? |
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| 18)
What are the x-intercept and the y-intercept of the given equation? State the intercepts as ordered pairs. |
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Equations Containing One Variable |
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| 19)
Complete the table below by putting four different values in for “y”. Do NOT make any calculations.Write the ordered pairs for these points and graph them. Draw a straight line through the points. This is the graph of “x = – 4”. Which statement best describes the graph? |
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| 20)
Complete the table below by putting four different values in for “x”. Do NOT make any calculations. Write the ordered pairs for these points and graph them. Draw a straight line through the points. This is the graph of “y = – 4”. Which statement best describes the graph? |
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The graphs of the equations given in the next three problems are shown below as they would appear on a graphing calculator. The x-axis and the y-axis are located in the center of the graphs and each notch on the axes represents one unit. State the letter of the graph that matches each equation. (Note: The graph of each line is highlighted for clarity.) |
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For the next two problems, use the “vertical line” test to determine if the graphs of relations are functions. If the graph is not a function, please explain why. |
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| 24)
Function? |
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| 25)
Function? |
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Refer to the following scenario to answer the next four questions: Brandon makes and sells car speakers. The fixed cost for his work space is $2000. The cost of materials and labor to build the speakers is $98 per set. Brandon sells the speakers for $150 per set. |
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| 30)
State two functions to represent Brandon’s income i(x) and his total costs c(x). |
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| 31)
Brandon’s profit is the difference between his income and his total costs. State a function to represent Brandon’s profit, p(x). |
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| 34) If you were directed by your school to complete Offline Activities for this course, please enter the information on the Log Entry form. |
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