Which of the following is the range of the function f(x) = x^2?
Practice Questions
Q1
Which of the following is the range of the function f(x) = x^2?
All real numbers
All positive real numbers
All non-negative real numbers
All integers
Questions & Step-by-Step Solutions
Which of the following is the range of the function f(x) = x^2?
Step 1: Understand the function f(x) = x^2. This means for any value of x, you will square it.
Step 2: Recognize that squaring any real number (positive, negative, or zero) will always give you a non-negative result. For example, if x = 2, then f(2) = 2^2 = 4; if x = -2, then f(-2) = (-2)^2 = 4; and if x = 0, then f(0) = 0^2 = 0.
Step 3: Since squaring a number cannot produce a negative result, the smallest value f(x) can take is 0 (when x = 0).
Step 4: As x increases or decreases, f(x) = x^2 will keep increasing without bound, meaning it can take any value from 0 to positive infinity.
Step 5: Therefore, the range of the function f(x) = x^2 is all non-negative real numbers, which can be written as [0, ∞).
