How To Do Functions Math

A math function is a one of the type of relation. In a function, no 2 ordered pairs can have the same 1st element and a different second element. The mathematical concept of a function expresses the intuitive idea that one quantity (the argument of the function, also known as the input) completely determines another quantity (the value, or the output). A function assigns a unique value to each input of a specified type. The math functions example problems and practice problems are given below. Source: Wikipedia

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Example problems for math functions:

Example problem 1:

        Show that the graph of x² + y² = 4 is not the graph of a function.

Solution:

       Clearly the equation x² + y² = 4 represents a circle with radius 2 and centre at the origin. Take x = 1

                         y² = 4 − 1 = 3

                         y = ± 3

For the same value x = 1, we have two y-values √3 and − √3 . It violates the definition of a function. the line x = 1 meets the curve at two places (1, √3) and (1, − √3) . Hence, the graph of x² + y² = 4 is not a graph of a function.

Example problem 2:

        Solve f(x) = 2x² − 12x + 50 ≤ 0 or find the domain of the function f(x).

Solution:

                2x² − 12x + 50 ≤ 0

                2(x² − 6x + 25) ≤ 0

                x² − 6x + 25 ≤ 0

               (x² − 6x + 9) + 25 − 9 ≤ 0

               (x − 3) ² + 16 ≤ 0

         This is not true for any real value of x.

         Given inequation has no solution

Example problem 3:

         Let A = {1, 4, 9}, B = {–1, –2, –3, –4, 1, 2, 3, 4}. If R = {(1, 1), (4,2), (9,3), (1, –1), (4, –2), (9, –3)} is a relation from A to B describe the relation by means of an arrow diagram. What is the relations represented by R?

Solution:

             In R, the ordered pairs may be considered as (1, 1), (1, –1), (4, 2), (4, –2), (9, 3) and (9, –3). Thus the first member is the square of the second member in every ordered pair. It follows that R represents the relation “ is the square of “ from A to B.

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Practice problems for math functions:

Practice problem 1:

         In the set N of natural numbers, define the relation R by x Ry if x + y = 9. Find n(R).

              Solution: n(R) = 8.

Practice problem 2:

          If R is a relation defined by “ is a factor of ” from A = {2, 4, 5} to B = {4, 6,10}, represent R (i) as a set of ordered pairs

        Answer: (i) set of ordered pairs, R = {(2,4), (2,6), (2,10), (4,4), (5,10)}