The function f(x) = 2x + 3 is continuous at which of the following? (2023)

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Question: The function f(x) = 2x + 3 is continuous at which of the following? (2023)

Options:

Correct Answer: All of the above

Exam Year: 2023

Solution:

f(x) = 2x + 3 is a linear function and is continuous for all x.

The function f(x) = 2x + 3 is continuous at which of the following? (2023)

The function f(x) = 2x + 3 is continuous at which of the following? (2023)

Step 1: Understand what a function is. A function takes an input (x) and gives an output (f(x)).
Step 2: Look at the function given: f(x) = 2x + 3. This means for any value of x, you can find f(x) by multiplying x by 2 and then adding 3.
Step 3: Identify the type of function. The function f(x) = 2x + 3 is a linear function because it can be represented as a straight line on a graph.
Step 4: Know the property of linear functions. Linear functions are continuous everywhere, meaning there are no breaks, jumps, or holes in the graph.
Step 5: Conclude that since f(x) = 2x + 3 is a linear function, it is continuous for all values of x.

Continuity of Functions – Understanding that linear functions, such as f(x) = 2x + 3, are continuous everywhere on their domain.