Question

Which of the following describes the graph of y = StartRoot negative 4 x minus 36 EndRoot compared to the parent square root function?
stretched by a factor of 2, reflected over the x-axis, and translated 9 units right
stretched by a factor of 2, reflected over the x-axis, and translated 9 units left
stretched by a factor of 2, reflected over the y-axis, and translated 9 units right
stretched by a factor of 2, reflected over the y-axis, and translated 9 units left

Answer 1

y = √(-4x - 36) = √[-4(x + 9)] = 2·√[-(x + 9)].

This is a vertical stretch by factor 2, a reflection across the y-axis (the minus inside), and a translation 9 units left (x+9).

So: stretched by a factor of 2, reflected over the y-axis, and translated 9 units left.