How to find the domain and range if a function

Question

h(x)=8-|x+4| range

f(x)= x^2-6x+14 domain.

Answer 1

1).

h ( x ) = 8 - | x + 4 |.

Domain of h ( x ) is the set of all real numbers.

Since, | x + 4 | is either positive or zero for x = - 4, the range of h ( x ) is given by the interval [0, - infinity].

2).

f ( x) = x^2 - 6x + 14.

The function f ( x) = x^2 - 6x + 14 is a quadratic function or parabola function.There are no rational or radical expressions, so there is nothing that will restrict the domain. Any real number can be used for x to get a meaningful output.

The domain of f ( x) = x^2 - 6x + 14 is all real numbers.