Question

Determine the domain and range of the following parabolaf(x)=2(x+6)^2+5

Answer 1

The given function is,

`y=2\mleft(x+6\mright)^2+5`

The function f(x) is defined at all points in the real number system.

The domain is the set of all points for the which the function is defined and real.

Therefore, the domain of f(x) is (-∞, ∞).

The range is the set of all defined values of the function.

Since a constant 5 is added to the square term of the function, the function will have values equal to or greater than 5.

So, the range of f(x) is [5, ∞).