Graph y = square root of x+4

Problem

y=√(,x+4)

Solution

1. Identify the parent function and the transformation. The parent function is y=√(,x) The expression x+4 inside the square root indicates a horizontal shift to the left by 4 units.

2. Determine the domain of the function. Since the value inside a square root must be non-negative, we set x+4≥0 which results in x≥−4

3. Find the starting point (vertex) of the graph. When x=−4 y=√(,−4+4)=0 The starting point is (−4,0)

4. Calculate additional points to determine the shape of the curve.

• If x=−3 y=√(,−3+4)=1 Point: (−3,1)

• If x=0 y=√(,0+4)=2 Point: (0,2)

• If x=5 y=√(,5+4)=3 Point: (5,3)

5. Plot the points on a coordinate plane and draw a smooth curve starting from (−4,0) and passing through the calculated points, extending to the right.

Final Answer

y=√(,x+4)

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