Answer:
The correct option is d: All real numbers.
Step-by-step explanation:
For a function f(x), the domain is the set of all the possible values of x that we can input in that function.
A general way to find the domain of a function is:
First, assume that the domain is the set of all real numbers.
Then, look at restrictions implied:
like in functions like:
f(x) = 4 if x > 3
Here the domain of the function is implied.
Third, let's find values of x that make "problems" with our function (for example, a zero in the denominator) and then remove these points from the domain.
In this case, we have a quadratic function:
y = a*x^2 + b*x + c
Here we do not have any problem (like a zero in a denominator), and we do not have any restrictions (We only know that the parabola is U shaped, so it is a function, and that its vertex is (2, 3) )
Then we can conclude that the domain of this function is the set of all real numbers.
The correct option is d: All real numbers.
