Question

1. (0 points) write the equation of the function where (h(x) = \sqrt{x}) has been reflected through the (x)-axis, reflected through the (y)-axis and shifted up by 5 units.

Explanation:

Step1: Apply reflection through the x-axis

Multiply the function by \(-1\):

$$y = -\sqrt{x}$$

Step2: Apply reflection through the y-axis

Replace \(x\) with \(-x\):

$$y = -\sqrt{-x}$$

Step3: Apply upward vertical shift

Add \(5\) to the function:

$$y = -\sqrt{-x} + 5$$

Answer:

\(y = -\sqrt{-x} + 5\)