Questions: y = √x - 2

Transcript text: 6) $y=\sqrt{x}-2$

Solution

Solution Steps

Step 1: Identify the parent function

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

Step 2: Determine the transformations

The given function is $y = \sqrt{x} - 2$. This represents a vertical shift of the parent function 2 units down.

Step 3: Plot the transformed function

Start with the parent function, $y = \sqrt{x}$. Some key points are (0, 0), (1, 1), (4, 2), (9, 3).

Shift each of these points down by 2 units to get the corresponding points for $y = \sqrt{x} - 2$: (0, -2), (1, -1), (4, 0), (9, 1).

Plot these points on the graph and draw a smooth curve through them.

Final Answer:

The graph of the function $y = \sqrt{x} - 2$ is the graph of $y = \sqrt{x}$ shifted 2 units down. Key points include (0,-2), (1,-1), (4,0) and (9,1). $\boxed{y = \sqrt{x}-2}$

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