The parent fifth-root function is given by f(x) = √[5]√[x]. Here are its key characteristics:
Domain: The domain of the function is all real numbers greater than or equal to 0. (x ≥ 0)
Range: The range of the function is all real numbers. (-∞ < f(x) < ∞)
Intervals of Increase: The function is strictly increasing for all positive real numbers. (x > 0)
Intervals of Decrease: The function is strictly decreasing for all negative real numbers. (x < 0)
Intervals of Constant: The function is constant at x = 0.
Intercepts: The x-intercept occurs at (0, 0), and there is no y-intercept since the function does not intersect the y-axis.
Even or Odd: Since f(-x) = -(f(x)), the function is odd.
Continuity: The fifth-root function is continuous for all real numbers.
Asymptotes: There are no asymptotes for this function.
End Behavior: As x approaches positive or negative infinity, f(x) also approaches positive or negative infinity, respectively.
Identify the key characteristics of the parent fifth-root function f left parenthesis x right parenthesis equals root index 5 start root x end root. 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.
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