determine the domain and range:{(x,y)|y2=5x}
To determine the domain and range of the equation {(x,y)|y^2=5x}, we can start by examining the given equation.
The equation y^2 = 5x represents a parabola. It is a quadratic equation with y as the dependent variable and x as the independent variable.
To find the domain, we need to identify the possible values for x. Since the equation does not have any restrictions on x, the domain is all real numbers. Therefore, the domain is (-∞, ∞).
To find the range, we need to determine the possible values for y. By analyzing the equation, we observe that y^2 must be greater than or equal to zero to satisfy the equation. This means that 5x must also be greater than or equal to zero. Since x is a real number, it can only be positive or zero when 5x is positive or zero.
Thus, the range of y is also greater than or equal to zero. In other words, the range is [0, ∞).
Therefore, the domain is (-∞, ∞) and the range is [0, ∞).