What is the domain of the function graphed below?

The graphed function's domain is . Correct answer: Option (a).

Further clarifications:

The domain encompasses all potential values that the function can assume. Specifically, the locations where the function holds true are referred to as the domain.

The range represents the values that result from the function's operation.

In summary, the output values are classified as range, while the input values where the function is valid are termed the domain.

Additional explanation:

The function cannot accommodate values of x that are equal to or exceed 7.

Thus, the function is operative for x values that are less than 7. As a result, the domain is .

The domain of the graphed function amounts to . Correct answer: Option (a).

Option (a) is indeed correct since it describes the domain of the graphed function as .

In contrast, Option (b) is incorrect, as the domain defined by the graph is .

Option (c) is not right either, as the domain identified in the graph is .

Likewise, Option (d) is also incorrect since it does not correspond to the domain indicated by the graph .

To learn more:

1. Discover details about the inverse of a function .

2. Explore information about the equation of a circle .

3. Understand the range and domain of functions

Answer Summary:

Grade: Middle School

Subject: Mathematics

Chapter: Functions

Keywords: range, domain, codomain, relation, function, graph, coordinates, open interval, closed interval, values.

The function is applicable within the segments of x:
(-∞, -1) and [-1, 7), meaning it is valid for x < 7.

Importantly,
the function cannot be evaluated at x = -1 in the left part of the linear graph, while it is valid at x = -1 in the right segment of the same line. Additionally, the function is not defined at x = 7 or any value above it.

Conclusion: x < 7.