which of the following is the graph of this square root function? f(x) = \\sqrt{x + 5}-2
which of the following is the graph of this square root function? f(x) = \\sqrt{x + 5}-2
Answer
- Domain:
- For the square - root function (y = \sqrt{x + 5}-2), the expression inside the square - root must be non - negative. So (x+5\geq0), which gives (x\geq - 5).
- Intercepts:
- x - intercept: Set (y = 0), then (\sqrt{x + 5}-2=0). Add 2 to both sides: (\sqrt{x + 5}=2). Square both sides: (x + 5 = 4), so (x=-1).
- y - intercept: Set (x = 0), then (y=\sqrt{0 + 5}-2=\sqrt{5}-2\approx2.24 - 2 = 0.24).
- Shape:
- The parent function of (y=\sqrt{x + 5}-2) is (y = \sqrt{x}), which has a shape that starts at the origin ((0,0)) and increases slowly. The function (y=\sqrt{x + 5}-2) is a horizontal shift of (y = \sqrt{x}) to the left by 5 units and a vertical shift down by 2 units.
The graph starts at the point ((-5,-2)) (since when (x=-5), (y=\sqrt{-5 + 5}-2=-2)) and passes through the point ((-1,0)) (x - intercept) and ((0,\sqrt{5}-2)) (y - intercept) and increases as (x) increases.
Since no options are labeled, we can't give a letter - based answer. But the correct graph is the one that has a starting point at ((-5,-2)), passes through ((-1,0)) and ((0,\sqrt{5}-2)) and has the shape of a square - root function (a curve that starts at a point and increases slowly for (x\geq - 5)).