2015-11-03 10:37:36
Find the range of the function. f(x) = (x - 2)^2 + 2
2015-11-03 14:29:11

The range which is also known as the codomain is defined as the set {f(x) | x E D}, which means all possible f(x) values given the input domain D. Domain: x spans all the real numbers in this equation. Expanding the equation gives: f(x)=x^2 - 4x +6 Since x^2 > 0 we know f(x) is a positively concaved parabola. That means it has no maximum value y can take, only a minimum. The minimum y value occurs at the vertex: -b/2a = 4/2 = 2 We are interested in the value of f(x) at x=2, f(2)=2. Therefore the range is: {f(x)>=2, f(x) E R} I provided a systematic way of solving this, but this can be solved by just observing the equation. It can be seen that the minimum value of y is 2. From that you can come to the same conclusion.