Which of the following describes the range of the function f(x) = x^2?

Practice Questions

Q1
Which of the following describes the range of the function f(x) = x^2?
  1. All real numbers.
  2. All positive real numbers.
  3. All non-negative real numbers.
  4. All integers.

Questions & Step-by-Step Solutions

Which of the following describes the range of the function f(x) = x^2?
  • Step 1: Understand what a function is. A function takes an input (x) and gives an output (f(x)).
  • Step 2: Look at the function f(x) = x^2. This means for any value of x, you square it to find f(x).
  • Step 3: Consider different values of x. For example, if x = 2, then f(2) = 2^2 = 4. If x = -2, then f(-2) = (-2)^2 = 4. If x = 0, then f(0) = 0^2 = 0.
  • Step 4: Notice that squaring any number (positive, negative, or zero) will always give you a result that is zero or positive.
  • Step 5: Since the output (f(x)) can never be negative, the smallest value it can be is 0.
  • Step 6: Therefore, the range of the function f(x) = x^2 includes all numbers from 0 to positive infinity.
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