Final answer:
The parent square root function increases for all x where x ≥0, which is represented as f(x) = √x. This function is always increasing on the interval [0, ∞). The function's increasing nature can also be utilized in solving right triangle problems and certain types of temperature calculations.
Step-by-step explanation:
The parent square root function increases for all x when x is greater than or equal to zero. In other words, the function f(x) = √x is an increasing function on the interval [0, ∞).
This is because as x increases, the value of the square root of x also increases, but at a decreasing rate since the curve flattens as x gets larger. Considering a right triangle with sides a and b and hypotenuse c, using the Pythagorean Theorem, and then 'undoing' the square by taking the square root, can illustrate this.
Similarly, for solving temperature problems where T is raised to the fourth power, taking the fourth root of T or raising T to the 0.25 power is necessary.