The function f(x) = 2x + 3 is continuous at which of the following intervals?

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Question: The function f(x) = 2x + 3 is continuous at which of the following intervals?

Options:

Correct Answer: (-∞, ∞)

Solution:

f(x) = 2x + 3 is a linear function and is continuous over the entire real line (-∞, ∞).

The function f(x) = 2x + 3 is continuous at which of the following intervals?

The function f(x) = 2x + 3 is continuous at which of the following intervals?

Step 1: Understand what a continuous function is. A function is continuous if you can draw it without lifting your pencil from the paper.
Step 2: Identify the type of function given. The function f(x) = 2x + 3 is a linear function, which means it forms a straight line when graphed.
Step 3: Know that linear functions are continuous everywhere. This means there are no breaks, jumps, or holes in the graph.
Step 4: Conclude that since f(x) = 2x + 3 is a linear function, it is continuous over the entire real line, which is represented as (-∞, ∞).

Continuity of Functions – Understanding that linear functions are continuous everywhere on the real number line.