If f(x) = x^2 + 3x + 2, what is f(1) and is it continuous?

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Question: If f(x) = x^2 + 3x + 2, what is f(1) and is it continuous?

Options:

Correct Answer: 6, Continuous

Solution:

f(1) = 1^2 + 3(1) + 2 = 6. Since f(x) is a polynomial function, it is continuous everywhere.

If f(x) = x^2 + 3x + 2, what is f(1) and is it continuous?

If f(x) = x^2 + 3x + 2, what is f(1) and is it continuous?

Step 1: Identify the function f(x) = x^2 + 3x + 2.
Step 2: Substitute x with 1 in the function to find f(1).
Step 3: Calculate f(1) by performing the operations: 1^2 + 3(1) + 2.
Step 4: Compute 1^2 which equals 1.
Step 5: Compute 3(1) which equals 3.
Step 6: Add the results from Step 4 and Step 5 to 2: 1 + 3 + 2.
Step 7: The final result is 6, so f(1) = 6.
Step 8: Determine if the function is continuous. Since f(x) is a polynomial function, it is continuous everywhere.

Function Evaluation – The process of substituting a specific value into a function to find its output.
Continuity of Functions – Understanding that polynomial functions are continuous everywhere on their domain.