Final answer:
The equation of the square root function that is reflected across the x-axis, dilated by a factor of 2, shifted 5 units to the right, and 3 units up is y = -2√(x-5) + 3.
Step-by-step explanation:
To begin by writing the equation of the square root function, which is y = √x. This function is reflected across the x-axis, dilated by a factor of 2, shifted 5 units to the right, and 3 units up.
We take the negative of the function to mirror it across the x-axis, and the resultant equation is y = -√x.
We multiply the function by two to dilate it by a factor of two, and the resultant equation is y = -2√x.
The equation becomes y = -2√(x-5) after we remove 5 from the x-values to move it 5 units to the right.
The final equation is y = -2√(x-5) + 3, which is achieved by adding 3 to the y-values in order to shift them up by 3 units.