1 In your own words describe what a function is Show an exam

1: In your own words, describe what a function is. Show an example of a function.? 2:How can you determine the domain and range of a function? Give an example and explain. ? 3: How does your strategy for factoring equations differ from factoring polynomial expressions?

Solution

1.Solution: Function is the relation between two sets where all the elements of first set (domain) is uniquely associated with the elements of the second set (codomain).

Example: f(x) = 2x+3 is a function f : R-->R.

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2.Solution: The set of all first components of the ordered pairs belonging to function is called the domain of function and the set of all second components of the ordered pairs is called the range of function.

In the above example the function is defined for all real values of x.

f(x) = 2x+3

When x = 1, then f(1) = 2(1)+3 = 5.

When x = 2, then f(2) = 2(2)+3 = 7 and so on.

Thus domain is all the real numbers.

When we subtitute the these values of x, we get corrosponding real values for f(x).

Thus range is also all the real numbers.

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3. Solution: If polynomial is a trinomial and if the coefficient of leading term is 1, then follow the following strategy to factor:

1. Write all pair factors of the constant term.

2. Selects only those pair of factors which on addtion or subtraction gives the middle terms.

3. Now splite the middle terms in two terms.

4. If there is common in the first two terms then take common. Similarly take common in the last two term if there is any.

5. Finally take common and then we will get the factors.