Question: What is the range of the function f(x) = x^2?
Options:
(-∞, ∞)
[0, ∞)
(-∞, 0)
[0, 1]
Correct Answer: [0, ∞)
Solution:
The function f(x) = x^2 has a minimum value of 0, so its range is [0, ∞).
What is the range of the function f(x) = x^2?
Practice Questions
Q1
What is the range of the function f(x) = x^2?
(-∞, ∞)
[0, ∞)
(-∞, 0)
[0, 1]
Questions & Step-by-Step Solutions
What is the range of the function f(x) = x^2?
Step 1: Understand what the function f(x) = x^2 means. It means that for any value of x, you square it (multiply it by itself).
Step 2: Identify the smallest value that f(x) can take. Since squaring any real number (positive or negative) will never give a negative result, the smallest value is 0.
Step 3: Recognize that as x gets larger (positive or negative), f(x) = x^2 also gets larger without any limit. This means it can go to infinity.
Step 4: Combine the information from Steps 2 and 3. The smallest value is 0, and it can go up to infinity.
Step 5: Write the range in interval notation. The range of f(x) = x^2 is [0, ∞).
No concepts available.
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