To obtain the graph of y=-3sqrt(x+1) from the basic graph y=sqrt(x) the transformations are first a stretch vertically by 3, then a reflection vertically, followed by a shift left of one...true or false?

shift left...Yes, true.

False. The correct sequence of transformations to obtain the graph of y=-3sqrt(x+1) from the basic graph y=sqrt(x) involves a shift left of one unit, followed by a vertical stretch by a factor of 3, and then a reflection vertically.

Here's a step-by-step breakdown of the transformations:

1. Horizontal Shift: The expression x+1 inside the square root causes a horizontal shift of one unit to the left. This means that each point on the original graph is shifted one unit to the left to obtain the new graph.

2. Vertical Stretch: The coefficient -3 in front of the square root causes a vertical stretch by a factor of 3. This means that each y-coordinate on the original graph is multiplied by -3, stretching the graph vertically.

3. Vertical Reflection: The negative sign in front of the square root causes a reflection vertically. This means that the entire graph is flipped over the x-axis, giving it a downward orientation.

Therefore, the correct sequence of transformations is a shift left of one unit, followed by a vertical stretch by a factor of 3, and then a reflection vertically.