consider the following function.\n\n p(x)=-2 sqrt{x-3}-1 \n\nstep 1 of 2: graph the original function by…

consider the following function.\n\n p(x)=-2 sqrt{x-3}-1 \n\nstep 1 of 2: graph the original function by indicating how the more basic function has been shifted, reflected, stretched, or compressed.\n\nanswer\n\nselect the type of transformations to create the correct graph. any further inputs required to complete the transformations will appear when the appropriate selection is made.\n\nhorizontal shift\n\nvertical stretch/compress\n\nx - axis reflection

consider the following function.\n\n p(x)=-2 sqrt{x-3}-1 \n\nstep 1 of 2: graph the original function by indicating how the more basic function has been shifted, reflected, stretched, or compressed.\n\nanswer\n\nselect the type of transformations to create the correct graph. any further inputs required to complete the transformations will appear when the appropriate selection is made.\n\nhorizontal shift\n\nvertical stretch/compress\n\nx - axis reflection

Answer

Explanation:

Step 1: Identify the basic function

The basic function is (y = \sqrt{x}).

Step 2: Analyze the horizontal shift

For the function (p(x)=-2\sqrt{x - 3}-1), comparing with (y=\sqrt{x - h}+k) (for horizontal shift (h)), here (h = 3). Since (h>0), the graph of (y = \sqrt{x}) is shifted to the right by 3 units.

Step 3: Analyze the vertical stretch/compress

The coefficient of (\sqrt{x-3}) is (- 2). The absolute value (|a|=2>1), so the graph of (y=\sqrt{x}) (after horizontal shift) is vertically stretched by a factor of 2.

Step 4: Analyze the (x) - axis reflection

Since the coefficient of (\sqrt{x - 3}) is negative ((a=-2)), the graph (after horizontal shift and vertical stretch) is reflected about the (x) - axis.

Step 5: Analyze the vertical shift

Comparing (p(x)=-2\sqrt{x - 3}-1) with (y=a\sqrt{x - h}+k), here (k=-1). So the graph (after previous transformations) is shifted down by 1 unit.

For the given options in the problem (horizontal shift, vertical stretch/compress, (x) - axis reflection):

  • Horizontal Shift: Right (because of (x-3) in the square - root function)
  • Vertical Stretch/Compress: Stretch (because (| - 2|=2>1))
  • (x) - Axis Reflection: Yes (because of the negative sign in front of the square - root function)

Answer:

Horizontal Shift: Right, Vertical Stretch/Compress: Stretch, (x) - Axis Reflection: Yes.