Graph f(x) = fourth root of x

Problem

ƒ(x)=√(4,x)

Solution

1. Identify the domain of the function. Since the index of the root is even, the radicand must be non-negative.

Domain: *x≥0

2. Determine the range of the function. The principal fourth root of a non-negative number is always non-negative.

Range: *y≥0

3. Calculate key points to plot on the coordinate plane by choosing perfect fourth powers for x

ƒ(0)=√(4,0)=0

ƒ(1)=√(4,1)=1

ƒ(16)=√(4,16)=2

ƒ(81)=√(4,81)=3

4. Analyze the shape of the curve. The function starts at the origin (0,0) and increases slowly as x increases, similar to the square root function but with a flatter curve for x>1

5. Sketch the graph by plotting the points (0,0) (1,1) and (16,2) and drawing a smooth curve through them starting from the origin and extending to the right.

Final Answer

ƒ(x)=√(4,x)

Want more problems? Check here!