THe domain of the function y=X2+3 is the set of all real numbers. What is the range of the function?
The minimum x^2 is zero, so the minimum y is 3 So the range is from 3 to inf.
2+2=
x+6/2x
To determine the range of the function y = x^2 + 3, we need to analyze the behavior of the function as x varies.
Since the function is a quadratic function with a positive coefficient of x^2, its graph opens upward, indicating that the minimum y-value occurs at the vertex of the parabola.
The x-coordinate of the vertex can be found using the formula x = -b/2a, where a and b are the coefficients of the quadratic equation. In this case, a = 1 and b = 0, so x = -0/(2*1) = 0.
Plugging the x-coordinate of the vertex (x = 0) into the function, we get y = (0)^2 + 3 = 3.
Therefore, the minimum value of y is 3, and there is no maximum value for y since the function continues to increase as x approaches infinity.
In conclusion, the range of the function y = x^2 + 3 is all real numbers greater than or equal to 3, or [3, ∞).