f(x)=x^2+4
set range of function
The range of the function f(x) =x^2+4 is all real numbers greater than or equal to 4.
Explanation:
To find the range of a function, we need to determine the set of all possible output values. In this case, the output value is f(x), which is equal to x^2+4.
Since the square of any real number is always non-negative (i.e., it is either zero or positive), the minimum value of x^2 is 0. Therefore, the minimum value of f(x) is 4 (when x=0).
As x increases, f(x) increases as well, because the square of a number greater than zero is always greater than zero. This means that the range of f(x) includes all real numbers greater than or equal to 4, but does not include any negative values.
Thus, the range of the function f(x) =x^2+4 is [4,∞).
To set the range of a function, we need to determine the minimum and maximum values that the function can take.
The given function is a parabolic function, which is a quadratic function of the form f(x) = ax^2 + bx + c, where a > 0. In this case, the function is:
f(x) = x^2 + 4
This is a parabola that opens upward (since the coefficient of x^2 is positive) and has its vertex at (0, 4). This means that the minimum value of the function occurs when x = 0 and f(0) = 4.
Since the parabola opens upward, there is no maximum value for the function; it increases without bound as x goes to positive or negative infinity.
Therefore, the range of the function is [4, +∞). This means that the function takes on all values greater than or equal to 4.