Question

what is the domain of this quadratic function?
options:
{ x | x ≤ 3 }
{ x | x ≤ 4 }
{ x | -3 ≤ x ≤ 1 }
all real numbers

Explanation:

Step1: Recall domain definition

The domain of a function is the set of all possible x - values for which the function is defined. For a quadratic function (which is a polynomial function), the graph is a parabola. Polynomial functions are defined for all real numbers because there are no restrictions on the input values (such as division by zero or taking the square root of a negative number) that would limit the x - values.

Step2: Analyze the quadratic graph

Looking at the graph of the quadratic function (the parabola), we can see that the parabola extends infinitely to the left and to the right along the x - axis. There are no breaks or restrictions on the x - values that we can plug into the quadratic function. So, the set of all x - values for this quadratic function includes every real number.

Answer:

all real numbers