how do I find the domain?

Question

state the domain of g(x)=1/4+6x. use interval notation to describe the domain, show your work.

Answer 1

The "domain" is all of the x-values that you can plug into the equation that result in a valid g(x) (y value). IN this case, g(x) is a linear function which is defined for all values of x. What that means is that I can put any value of x into the equation and compute a valid y-value. For example, fo x = -1/2:

g(x) = 1/4 + 6x

g(x) = 1/4 _ 6·(-1/2)

g(x) = 1/4 - 3

g(x) = -2 3/4

So I plugged in x = -1/2 and was able to get a value for g(x). In this case, If you look at the equation, you can multiply any value of x by 6 then add 1/4 to it, so all values of x work. In fact, g(x) is a linear equation and the domain for linear equation is all values of x from negative infinity to positive infinity; that is you can plug in any value of x and get a value for g(x). In interval notation, the domain of g(x) is (-∞,∞)