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| Introduction to Functions |
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1) Refer to the relation below to answer the following questions:
(a) What is the domain of the relation?
(b) What is the range of the relation? |
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| 2) Is the relation in the previous problem a function? Explain how you know that the relation is or is not a function. |
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| 3) For the ordered pairs given in the table, is the relation a function? |
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| 4) For the y-values in the given in the table, add x-values that will eliminate the set of ordered pairs as being a function. State the four x-values. |
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5) Use the vertical line test to determine if the graph is a function.
(a) Is the graph a function?
(b) Explain how you know that the graph is or is not a function. |
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6) Use the vertical line test to determine if the graph is a function.
(a) Is the graph a function?
(b) Explain how you know that the graph is or is not a function. |
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| 7) Evaluate the function below for (a) x = 3, and then (b) x = 7. |
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| 8) Evaluate the function below for (a) x = 0, and then (b) x = –2. |
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| Operations with Functions |
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| In the following problems, find the sum and the difference of the given functions. |
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| 9) What is the sum and difference of the given functions? |
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| 10) What is the sum and difference of the given functions? |
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| In the following problems, find the product and the quotient of the given functions. Determine the answers and any domain restrictions. |
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| 11) What is the product and quotient of the given functions? |
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12) What is the product and quotient of the given functions?
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| In the following problems, compose the functions as directed. |
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| 13) Compose the given functions as directed. |
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| 14) Compose the given functions as directed. |
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In the following problems, determine the following:
(a) state whether the relation is a function,
(b) find and state the inverse, and
(c) state whether the inverse is a function.
Recall: For the inverse function, switch the x- and y-coordinates. |
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| 15) {(0, 1), (1, 4), (2, 9), (3, 16)} |
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| 16) {(4, 5), (5, 10), (4, 6), (3, 2)} |
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17) For the ordered pairs given in the table, determine the following:
(a) state whether the relation is a function,
(b) find and state the inverse, and
(c) state whether the inverse is a function. |
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| 18) True or False. The graphs of the functions shown are inverses of each other. (The dotted line is the graph of y = x.) |
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| 19) True or False. The graphs of the functions shown are inverses of each other. (The dotted line is the graph of y = x.) |
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| Graph the following pairs of functions and the line y = x. Determine whether the functions are inverse functions. You may graph the functions on a graphing calculator or click here to navigate to an online graphing calculator. |
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| 20) Are these functions inverse functions? Please explain why or why not in reference to the line y = x. |
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| 21) Are these functions inverse functions? Please explain why or why not in reference to the line y = x. |
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| 22) Are these functions inverse functions? Please explain why or why not in reference to the line y = x. |
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| In the following questions, some of the equations require non-standard keyboard characters when entered. For these equations, write them similar to the examples illustrated below: |
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| In the following questions, use the Horizontal Line Test to determine if the graph of the inverse of the function given is a function. |
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| 25) True or False. This graph’s inverse is a function. |
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| 26) True or False. This graph’s inverse is a function. |
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27) Determine if the functions are inverses of each other by finding both of their compositions.
(a) What is the f (g (x))?
(b) What is the g (f (x)?
(c) Are the functions inverses of each other? (Recall that if both of the compositions of the functions equal x, then the functions are inverses of each other.) |
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28) Determine if the functions are inverses of each other by finding both of their compositions.
(a) What is the f (g (x))?
(b) What is the g (f (x)?
(c) Are the functions inverses of each other and why? |
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| 29) Explain the difference of the two expressions in the question. |
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| 30) Explain how the domain and range of a function compare to the domain and range of its inverse. |
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| 31) Compare and contrast the vertical line test and the horizontal line test. |
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| 33) How can you show through mathematical operation that functions are inverses of each other? |
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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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