Question

Given the function and the graph below, which of the following best describes the domain and range?

Answer 1

Step-by-step explanation

Let's analyze the formula of our function:

`f(x)=(-x-1)^2+3.`

Note that the expression on the right-hand side makes sense for any real number; then, the domain of f consists of all real numbers.

Now, let's analyze the graph of f:

Note that the function takes values ( "vertical values") from 3 up. The value three is included. Then, the range of the f consists of all y such that

`y\ge3.`

Answer

The domain of f consists of all real numbers.

The range of the f consists of all y such that

`y\ge3.`