Question - Solving Transformed Square Root Functions
mathfunction transformationstransformed square root functionsequation analysisvertical and horizontal shifts
Solution:
The equation provided appears to be in the form of a transformed square root function:y = A√(B(x - C)) + DWhere:- A represents the vertical stretch or compression and reflection over the x-axis.- B represents the horizontal stretch or compression and reflection over the y-axis.- C represents the horizontal shift (left or right).- D represents the vertical shift (up or down).For the given equation:y = 2√(x + 3) + 4We need to find the values of A, B, C, and D. It's important to note that the instruction specifies to find the OPPOSITE of what you see in the equation for B and C. That means we take the negative or opposite value of what we see next to x for C (usually given as x - C, but here we have x + 3, so C will be the opposite of 3) and potentially the opposite of the B value, though there's no B visible, implying B is 1 (the default multiplicative identity).Hence, the values are:A = 2 (because of the vertical stretch by a factor of 2)B = 1 (the value in front of the "(x + 3)" as there's no visible coefficient, it's understood to be 1)C = -3 (the OPPOSITE of +3, indicating a horizontal shift 3 units to the LEFT)D = 4 (the vertical shift upwards by 4 units)So, we have:A = 2B = 1C = -3D = 4
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