SOLUTION: I need help on solving this equation. I'm supposed to find the domain and range. I think that domain is x and range is y and that f(x) is the same thing as y. Therefore, I think t

Question 261456: I need help on solving this equation. I'm supposed to find the domain and range. I think that domain is x and range is y and that f(x) is the same thing as y. Therefore, I think that f(x) is the range and x is the domain. Here is the problem: f(x) = 2x + 4
Thank you for your time!
Found 2 solutions by jim_thompson5910, solver91311:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Domain: Set of all possible inputs
Range: Set of all possible outputs

Because 'x' is considered the input, we can think of the domain as the set of all 'x' values that we can plug in. Since there are no restrictions on what to plug in (we don't have to worry about dividing by zero), the domain is the set of all real numbers.

If we graph f(x) = 2x + 4, we will find that every 'y' value will get hit at some 'x' value. So the range is also the set of all real numbers.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Not quite. The domain of a function is the set of values that the independent variable (typically, and in this case, the such that the expression defining the function is defined. Generally you would want to ask what is the domain of the function over the Real Numbers (or some other specific set of numbers in some cases)

In the case of , can take on any real number value and will take on a corresponding real number value.

Hence, the domain is the set of all real numbers. Symbolically,

The range is the set of values that takes on for every possible value in the domain. In the case of your example, the range is also all real numbers.

Contrast this with a function such as:

Here the value 1 must be excluded from the domain because if , the denominator is zero and that makes the expression undefined. For this example, the domain is all real numbers EXCEPT 1.

Coincidentally, the range also excludes 1 for this example. Notice that no matter how large becomes, will never equal , so the fraction can never take on the exact value of 1.

Here's another example:

In this case we have to exclude any value for that would cause the radicand to be smaller than zero since the square root of a negative number is undefined in the real numbers. Hence the domain is found by

The range in this case is all positive numbers.

Of interest is the absolute value function:

Which has a domain of all reals, but a range of

Just as a general set of rules:

Any polynomial function has a domain of all real numbers. Polynomial functions of odd degree have ranges of all real numbers. Polynomial functions of even degree have either a minimum or maximum value which restricts their range.

Rational functions have their domain restricted by eliminating values that make a denominator equal zero.

Functions with radicals having a even index (square root, 4th root, etc.) are restricted to values of the independent variable that make the radicand greater than or equal to zero.

and have unrestricted domains but the range is restricted to values between -1 and 1 inclusive.

Exponential functions can take any real number as an input, but have a range strictly greater than zero.

Logarithmic functions have a domain restricted to reals strictly greater than zero. Furthermore, the base must be strictly greater than zero. The range is all real numbers.

John

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