Graph g(x)=3/4* fifth root of x

Problem

g(x)=3/4√(5,x)

Solution

1. Identify the parent function as ƒ(x)=√(5,x) which is an odd function defined for all real numbers x

2. Determine the domain and range, which are both (−∞,∞) because the index of the root is odd.

3. Analyze the transformation, where the factor 3/4 results in a vertical compression of the parent graph toward the xaxis.

4. Calculate key points to plot the curve:

   • If x=−32 g*(−32)=3/4*(−2)=−1.5

   • If x=−1 g*(−1)=3/4*(−1)=−0.75

   • If x=0 g(0)=0

   • If x=1 g(1)=3/4*(1)=0.75

   • If x=32 g(32)=3/4*(2)=1.5

5. Sketch the graph as a smooth curve passing through the origin (0,0) with an infinite vertical slope at that point, extending infinitely in both directions.

Final Answer

g(x)=3/4*x(1/5)

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