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The function f(x) = x^2 is continuous at which of the following points? (2023)
The function f(x) = x^2 is continuous at which of the following points? (2023)
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Practice Questions
1 question
Q1
The function f(x) = x^2 is continuous at which of the following points? (2023)
x = -1
x = 0
x = 1
All of the above
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The function f(x) = x^2 is a polynomial function and is continuous at all points, including -1, 0, and 1.
Questions & Step-by-step Solutions
1 item
Q
Q: The function f(x) = x^2 is continuous at which of the following points? (2023)
Solution:
The function f(x) = x^2 is a polynomial function and is continuous at all points, including -1, 0, and 1.
Steps: 5
Show Steps
Step 1: Understand what continuity means. A function is continuous at a point if you can draw it without lifting your pencil.
Step 2: Identify the function given, which is f(x) = x^2.
Step 3: Recognize that f(x) = x^2 is a polynomial function.
Step 4: Know that polynomial functions are continuous everywhere on the real number line.
Step 5: Conclude that since f(x) = x^2 is continuous everywhere, it is also continuous at the specific points -1, 0, and 1.
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