Functional Notation and Terminology: Practice Exercises

Here are various Exercises to accompany the section Functional Notation and Terminology.  

Functional Evaluation

  1. Evaluate each of the following functions at the given input value:
    1. Evaluate the function given by {(1, 0), (0, 0), (2, -0.4), (-1, -0.4), (3, -1.2), (-2, -1.2), (-3, -2.4)} using an input of 3.
    2. Evaluate the following function at t = 0.8:
      t h
      0
      0.2
      0.4
      0.6
      0.8
      1.
      1.2
      1.4      		 1.4
      2.4
      3
      3.2
      3
      2.4
      1.4
      0
    3. Evaluate the following function using an input of b:

    4. Evaluate the following function using an input of 2:

      Note: You will only be able to give an approximate answer.

    5. Evaluate the function given by the equation, h = 1.4 + 6t - 5t2, at t = 0.2.
    6. Evaluate the following function using an input of 2:

    7. Evaluate the function given by the rule: "Add 5 to the input, then multiply the result by the input," using an input of 3.

    Solution.

Functional Terminology

  1. For each of following functions, describe the set of values in the domain and range:
    1. The function with the arrow diagram:

    2. The function given by the following table:
      x y
      -3
      -2
      -1
      0
      1
      2       		5
      1
      -2
      1
      3
      4

    3. The function given by the following plot:

    Solution.

Functional Notation

  1. For each of the following functions, simplify the given functional expression:
    1. If the function f is given by {(1, 0), (0, 0), (2, -0.4), (-1, -0.4), (3, -1.2), (-2, -1.2), (-3, -2.4)}, compute f(2).
    2. If the function g is given by the table
      t u = g(t)
      0
      0.2
      0.4
      0.6
      0.8
      1.
      1.2
      1.4      		 1.4
      2.4
      3
      3.2
      3
      2.4
      1.4
      0
      compute g(0.4).
    3. If the function h is given by the arrow diagram:

      4. compute h(d). 

    4. If the function k is given by the graph:

      compute k(-2).  Note: You will only be able to give an approximate answer.

    5. If the function s is given by the equation, s(t) = 1.4 + 6t - 5t2, compute s(0.4).
    6. If the function q may be pictured by the following black-box diagram:

      compute q(3).

    7. If the function r is given by the rule: "Add 5 to the input, then multiply the result by the input," compute r(2).
    8. Compute id(5), where id is the identity function.

    Solution.

Go to Functions and Algebra .

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