Identify the key characteristics of the parent fifth-root function f(x)= 5 sqrt x. Include the following: domain, range, intervals where the function is increasing. decreasing, or constant, intercepts, whether the function is even, odd, or neither, whether the function is continuous or discontinuous, asymptotes, and end behavior.

I guess that would be p(x) = √x

since the domain is all x >= 0, it is always increasing
intercept is (0,0)
since f(-x) does not exist, it is neither even nor odd
now your turn for the rest

Did you know?

Did you know that the parent fifth-root function, f(x) = 5√x, has some interesting characteristics? Firstly, its domain consists of all non-negative real numbers, since the fifth root can only be taken of positive or zero values. The range of the function includes all non-negative real numbers as well, from zero to positive infinity. When it comes to intervals where the function is increasing, we find that it is increasing for all positive values of x. Conversely, the function is decreasing for x values between zero and one, and finally, it remains constant at zero. In terms of intercepts, the x-intercept occurs at the origin (0, 0), and there is no y-intercept as the function does not evaluate to a finite value at x = 0. Regarding symmetry, the parent fifth-root function is neither even nor odd. This means that it does not exhibit any specific symmetry about the y-axis or the origin. In terms of continuity, the function is continuous for all values of x within its domain, as there are no breaks or jumps in its graph. There are also no asymptotes present in the parent fifth-root function. Finally, when it comes to end behavior, the function approaches positive infinity as x approaches positive infinity, and approaches zero as x approaches zero from the right.