Questions: The graph of y=√x is given below: Find a formula for each of the transformations whose graphs are given below. a) y= b) y= c) y=

Transcript text: The graph of $y=\sqrt{x}$ is given below: Find a formula for each of the transformations whose graphs are given below. a) $y=$ $\square$ b) $y=$ $\square$ c) $y=$ $\square$

Solution

Solution Steps

Step 1: Identify the original function

The original function given is $ y = \sqrt{x} $.

Step 2: Analyze the transformation in part (a)

In part (a), the graph is shifted 2 units to the right. This transformation can be represented by replacing $ x $ with $ x - 2 $ in the original function.

Step 3: Write the formula for part (a)

The formula for the transformation in part (a) is: \[ y = \sqrt{x - 2} \]

Step 4: Analyze the transformation in part (b)

In part (b), the graph is reflected over the y-axis. This transformation can be represented by replacing $ x $ with $ -x $ in the original function.

Step 5: Write the formula for part (b)

The formula for the transformation in part (b) is: \[ y = \sqrt{-x} \]

Step 6: Analyze the transformation in part (c)

In part (c), the graph is shifted 3 units down. This transformation can be represented by subtracting 3 from the original function.

Step 7: Write the formula for part (c)

The formula for the transformation in part (c) is: \[ y = \sqrt{x} - 3 \]