Explain the Domain & Range of Functions

• Explain the domain and range of a function. Under what circumstances would the domain be something other than all real numbers? Provide an example.

Domain: The domain of a function is the set of ‘input’ values; the function must be well defined for these input values.
Range: The range of a function is the set of ‘output’ values that result after f is applied to every element of the domain. **The domain will NOT be all real numbers when the horizontal distance from the origin is zero;
Example: Consider the line of the form x=a, where a is any real number. Here the domain is {a}, and the range is all real numbers. (x represents the horizontal distance from the origin)

• What is a function, in your own words? Give an example of a function using the variable x and explain how we evaluate a function for a given value of x.

Function: While the definition of a function is actually somewhat complex, we can summarize the basics as follows: If we were to take all possible values of x and plug them into the equation & solve for y, we will get exactly one value for each value of x
Example of a function: y = x2- 5x + 3
Evaluating a function: is simply asking what its value is for specific values of x; or what is the value of y when given the value of x. – plug in the value of x and then solve the equation for y.