Question

Consider the following. Use the vertical Line Test to determine whether the curve is the graph of a function of x. Yes, the curve is a function of x. No, the curve is not a function of x. If the curve is a function, state the domain and range. (Enter your answers using interval notation. If the curve is not a function enter NoNE.) domain range

Answer 1

In interval notation, the domain of the function is [-2,1]. The range of the function is [-3,2].

Writing the domain and range of a graph.

In the given question, the domain is referred to as the set of all the real values of x(input values) for which the function is defined.

In the graph of the question attached below, we can see that the line approaches -2 and 1. Thus, the domain of the function is defined at -2 ≤ x ≤ 1. In interval notation, the domain is [-2,1]

The range of the function is the set of all the output values (y) that each values of x is assigned too. Thus, the range of the function approaches y-axis at 2 and -2. In interval notation, the range of the function is [-3,2].

The missing image in the question is attached below.

Answer 2

The graph of the function is a horizontal line, making it a function of x with a domain of [0, 20] and a range of 20.

Step-by-step explanation:

The graph of a linear equation of the form y = a + bx is a straight line. The graph represents a function of x if every vertical line intersects the graph at most once. This can be determined using the vertical line test. If the line intersects the graph at more than one point, then it is not a function.

In this case, the graph of the function f(x) is a horizontal line. Since the line is horizontal, it intersects every vertical line at exactly one point. Therefore, the curve is a function of x.

The domain of the function is [0, 20], as stated in the question. The range of the function is the set of all y-values that the function takes on. In this case, the range is the constant value of the horizontal line, which is simply 20.