If f(x) = x^2 + 2x + 1, what is f(-1)? Is f(x) continuous at x = -1? (2019)

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Question: If f(x) = x^2 + 2x + 1, what is f(-1)? Is f(x) continuous at x = -1? (2019)

Options:

Correct Answer: 1, Yes

Exam Year: 2019

Solution:

f(-1) = (-1)^2 + 2*(-1) + 1 = 0. The function is a polynomial and is continuous everywhere, including at x = -1.

If f(x) = x^2 + 2x + 1, what is f(-1)? Is f(x) continuous at x = -1? (2019)

If f(x) = x^2 + 2x + 1, what is f(-1)? Is f(x) continuous at x = -1? (2019)

Step 1: Identify the function f(x) = x^2 + 2x + 1.
Step 2: Substitute -1 into the function: f(-1) = (-1)^2 + 2*(-1) + 1.
Step 3: Calculate (-1)^2, which is 1.
Step 4: Calculate 2*(-1), which is -2.
Step 5: Now add the results: 1 - 2 + 1.
Step 6: Calculate 1 - 2 = -1, then -1 + 1 = 0.
Step 7: So, f(-1) = 0.
Step 8: Determine if f(x) is continuous at x = -1. Since f(x) is a polynomial, it is continuous everywhere.
Step 9: Conclude that f(x) is continuous at x = -1.

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.