Does anyone know quick (AND EASILY EXPLAINED) ways to find the domain of a function?

Question

For example, I know to find the domain of a fraction (1/x+2), you set the denominator equal to zero, and that number is NOT in the domain (ie- -2). But what about for functions like 2(x-3)? I am in a Calculus class and I am working on finding extremas, and whether sections are increasing or decreasing. I need a quick and easy way to look at a function and determine the domain.

Answer 1

First, if the function is definied as a set of points, the domain is just all the x's that are used. The domain of { (1,2),(3,4),(5,2) } is {1,3,5}.

Second, if the function is definied by a graph, the domain is all the x's that are covered on the graph and is usually expressed as an interval, like 0 < x < 5.

You seem to mostly be talking about functions that are defined by equations. When in doubt, the answer is "all real numbers", because that is the domain for the vast majority of functions. If the second function you describe is f(x)=2x(x-3) ... meaning 2x times x - 3, the domain is all real numbers. ALL polynomial functions (as well as sine and cosine, the other two big functions found in calculus) have a domain of all real numbers.

There are two main things that can screw up the domain. First are fractions. As you point out, you basically ask yourself what would make them undefined (set bottom = 0). If you're stating the domain, you'll almost certainly do so with intervals, such as negative infinity to negative 2 and negative 2 to positive infinity (for the first function you give).

The other big thing that can screw up a domain is even roots (or equivalent fractional exponents). These will give complex number answers if you input a negative number, so when treated as a real-number function, you restrict the domain to non-negative numbers. To do this take what's under the root and write out a statement that that expression is greater than or equal to zero. For example SQR(-3x + 2) would give you -3x + 2 >= 0. Solve that. For example, this problem would give x <= 2/3. This works for ALL square roots as well as fourth roots, sixth roots, quantities to the one-half power, etc.

Other things you might encounter in calculus:
exponential functions == All real numbers (they're definied for everything)
logarithmic functions == Undefined if the argument is 0. So set what's in the parentheses equal to 0, just like you would with the bottom of a fraction.
tangent == Undefined for odd multiples of pi/2. (Most often the domain is restricted to between -pi/2 and pi/2.)
reciprocal trig functions (sec, csc, cot) == Undefined when the defining function (cos, sin, tan) is equal to zero.
????? == Again, when in doubt, it's all real numbers.

Answer 2

If you want to find the domain, just think the function as a bus, and people as the X, then the Y or F(x) is going to be the bus stops. So when you want to find the domain, you should actually should find that where you can go with the bus, obviously you can't go under the water or when there is no bus stop you can't get out of the bus!
So when you want to find the domain of any function it is easier to find the Xs that you can't put in the function. For your case, it's a fraction and you know that a fraction can't be something over zero, so you need to find the Xs that lead the denominator be zero, as you said. Now on the other case you have 2(x-3); thnk about the Xs that can make this undefined or not acceptable? the only thing that make it undefined is infinty! and infinty is not a number so this function has real numbers IR as its domain, cause you actually can put any number insted of X and get an answer.
I hope i helped you

Answer 3

Just plug in the f(x) value for every x variable that pops up in the equation. For example, if it asks you to solve for f(x)=2x+4 when the domain is 3...then you do 2(3)+4 which equals 10! You plug in 3 wherever x shows up.

Answer 4

It usually is whatever the domain can't be, the zeroes, or where you get imaginary numbers.

For equations like, 2(x-3), just think to yourself about what numbers make this equation false, or wrong. Domain is all number that satisfy the equation, so, what numbers satisfy that equation? All of them.

Don't know if that helped any.

Answer 5

The area dictates the self reliant variable, and that shall we choose and limit it. frequently refers to x-axis. the variety is a based variable and is the tip results of substituting the cost of the area. frequently refers to y-axis. Ex. y = 2x - 3, area = (-a million

Answer 6

sorry just wanted to check the answers