If f(x) = 3x + 2, what is the value of f(2) and is it continuous?

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Question: If f(x) = 3x + 2, what is the value of f(2) and is it continuous?

Options:

Correct Answer: 8, Continuous

Solution:

f(2) = 3(2) + 2 = 8. Since f(x) is a polynomial, it is continuous everywhere.

If f(x) = 3x + 2, what is the value of f(2) and is it continuous?

If f(x) = 3x + 2, what is the value of f(2) and is it continuous?

Step 1: Identify the function given, which is f(x) = 3x + 2.
Step 2: Substitute the value of x with 2 in the function. This means we will calculate f(2).
Step 3: Calculate f(2) by replacing x with 2 in the equation: f(2) = 3(2) + 2.
Step 4: Perform the multiplication: 3 times 2 equals 6.
Step 5: Add 2 to the result from Step 4: 6 + 2 equals 8.
Step 6: Conclude that f(2) = 8.
Step 7: Determine if the function is continuous. Since f(x) is a polynomial (3x + 2), it is continuous everywhere.

Function Evaluation – The process of finding the output of a function for a given input.
Continuity of Functions – Understanding that polynomial functions are continuous everywhere on their domain.