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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| 9) What is the inverse of the point (x, y)?
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| 10) What is the inverse of the point (2, 5)?
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| 11) Fill in the table to reflect the inverse of the function. Type your answer so that it reflects the numbers from top to bottom.
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| 12) Given the ordered pairs in the table below, write the ordered pairs of the inverse function.
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| 13) Is the answer to #12 a function?
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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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| 14) { (2,3), (4,5), (5,4), (2,4) }
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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) Are these functions inverse functions?
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| 19) Are these functions inverse functions?
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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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| 20) For the function, find the equation of the inverse. Solve the new equation for y.
Hint: Switch x and y, and then solve for y.
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| 21) For the function, find the equation of the inverse. Solve the new equation for y.
Hint: Switch x and y, and then solve for y.
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| 22) For the function, find the equation of the inverse. Solve the new equation for y.
Hint: Switch x and y, and then solve for y.
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| 23) Explain how the domain and range of a function compare to the domain and range of its inverse.
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| 24) How do you find the inverse of a function? Explain the process?
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| 27) Find the discriminant and tell the number and type of solutions for 2x2 – x + 6 = 0.
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| 28) Solve x2 – 4x + 13 = 0. Type the solutions. A negative discriminant yields 2 imaginary solutions.
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| 29) Identify the direction of the opening, the vertex, and the axis of symmetry of the parabola of the equation given below.
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| 30) Graph the equation given below on a piece of graph paper, and then choose the correct graph for the equation. State the letter of the correct graph.
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| 31) Factor.
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| 32) Solve for “x” by factoring.
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| 33) Simplify.
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| 34) Multiply and state the answer in simplified form.
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| 35) Divide and state the answer in simplified form.
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| 36) Add and state the answer in simplified form.
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| 37) Solve for “x.”
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| 38) 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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