Question

Is y = 1/4x^0.5 a power function? Explain your reasoning.

Answer 1

The equation y = 1/4x^0.5 is a power function because it fits the general form of a power function, y = ax^n, with a constant coefficient and a real number exponent.

Step-by-step explanation:

Yes, the function y = 1/4x^0.5 is indeed a power function. A power function is of the form y = ax^n, where a is a constant and n is a real number, representing the power of x. In the given function, a is equal to 1/4, and n is 0.5, which is equivalent to the square root of x (since raising a number to the 0.5 power is the same as taking its square root).

Therefore, we can express the square root of x as x raised to the power of 1/2, fitting the form of a power function.

Answer 2

`y =\displaystyle(1)/(4)x^(0.5)`

It is a power function.

Step-by-step explanation:

We are given the following function in the question:

`y =\displaystyle(1)/(4)x^(0.5)`

We have to check whether the given function is a power function or not.

Power Functions :

• A power function is of the form:

`f(x) = ax^p,`

where a is a constant and not equal to zero and p is a real number.

Comparing the given function, we get:

`a = \displaystyle(1)/(4)\\\\p = 0.5`

Hence, the given function is a power function.