Question

Match the range of the function f(x) = x2 2x − 1 to its domain.

Answer 1

F(x) = x^2 + 2x -1

Domain all real number

Range: all real numbers equal or greater than -2.

To find the range you need to find the vertex of the parabole, which is (-1,-2) and use the fact that, given that the coefficient of x^2 is positive, the funcion open upwards (which means that the vertex is a global minimum).

To find the vertex you use the quadratic formula to find the roots and then the x-coordinate of the vertex is in the middle of the two roots.