state the domain of the following function in interval notation
f(x)=x^2-4x+3
plug in numbers to explain reasoning
The domain of the function f(x) = x^2 - 4x + 3 is all real numbers, or (-∞, ∞), because there are no restrictions on the values x can take in this function.
For any real number x, we can plug it into the function f(x) = x^2 - 4x + 3 and get a valid output. For example, if we plug in x = 0, we get f(0) = 0^2 - 4(0) + 3 = 3. If we plug in x = -1, we get f(-1) = (-1)^2 - 4(-1) + 3 = 8.
Since we can plug in any real number into the function and get a valid result, the domain of the function is all real numbers, or (-∞, ∞).