Graph y = square root of 7-x

Problem

y=√(,7−x)

Solution

1. Identify the domain by setting the expression inside the square root to be greater than or equal to zero.

7−x≥0

x≤7

2. Determine the starting point of the graph by substituting the boundary value of the domain.

y=√(,7−7)

y=0

The endpoint is (7,0)

3. Find the y-intercept by setting x=0

y=√(,7−0)

y=√(,7)≈2.65

4. Select additional points to determine the shape of the curve.
   If x=6 y=√(,7−6)=1
   If x=3 y=√(,7−3)=2
   If x=−2 y=√(,7−(−2))=3

5. Sketch the graph starting at (7,0) and drawing a smooth curve that passes through (6,1) (3,2) and (0,√(,7)) extending to the left as x decreases.

Final Answer

y=√(,7−x)

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