The range of the function is determined by the possible values of the output, given the inputs. In this case, the function f(x) = 3 – 4x + 4y represents a linear relationship between x and y.
To find the range, we should isolate y in terms of x. Rearranging the equation gives us:
4y = f(x) – 3 + 4x
So:
y = (f(x) – 3 + 4x) / 4
The key aspect of this function is that for any real number x, you can always find a corresponding y value by adjusting y with respect to the chosen x. Thus, as x varies over all real numbers, y can take any value in the real numbers as well.
Therefore, the range of the function f(x) is all real numbers, or (-∞, ∞).