Finding domain and range of functions?

Question

Ok the problem is:
F(x) = -x^2 - 2x + 3
Its asking me to state the domain and the range. Im totally blanking on this. What do i do?

Answer 1

As for the domain, if you're not dividing by 0 or taking the log of a negative, if any number can be x without choking a calculator, your domain is all real numbers.

Range is the output of the function, and since it's a quadratic, it has (in this case) a maximum value. When x = -1, y = 4, and for all other values of x, y < 4, so your range is (-∞, 4].

Answer 2

First thing you got to do is plot the graph on the calculator. You can use a graphics calculator or some web based application.

Domain = x value
Range = y value

This is the answer, in its proper notation:

Domain: {x : x is in R} (R = rational number)
Range: {y: Y > 2}

You use the graph to determine the domain and range of both the x and y functions. This function can have any x value, but only y values of 2 or greater.