Questions: Below is the graph of y=sqrt(x). Transform it to make it the graph of y=-sqrt(x+3)-1.

Transcript text: Below is the graph of $y=\sqrt{x}$. Transform it to make it the graph of $y=-\sqrt{x+3}-1$.

Solution

Solution Steps

Step 1: Shift the graph horizontally.

The transformation from $\sqrt{x}$ to $\sqrt{x+3}$ represents a horizontal shift to the left by 3 units. So, the point (0,0) becomes (-3,0).

Step 2: Reflect the graph across the x-axis.

The transformation from $\sqrt{x+3}$ to $-\sqrt{x+3}$ involves reflecting the graph over the x-axis. The point (-3,0) remains at (-3,0).

Step 3: Shift the graph vertically.

Finally, subtracting 1 shifts the entire graph down by one unit. This transforms $-\sqrt{x+3}$ to $-\sqrt{x+3}-1$. Thus, the point (-3,0) shifts to (-3,-1).

Final Answer:

The graph of $y = -\sqrt{x+3} - 1$ is obtained by shifting the graph of $y = \sqrt{x}$ three units left, reflecting it across the x-axis, and then shifting it down one unit.

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