Question

How does the graph of y=-3√2x-4 compare to the graph of y=-3√x-4?

The graph is stretched horizontally by a factor of 2 and then moved right 4.
The graph is compressed horizontally by a factor of 2 and then moved down 4.
The graph is compressed horizontally by a factor of 2, moved left 4, and moved down 4.
The graph is stretched horizontally by a factor of 2, moved left 4, and moved down 4.

Answer 1

Assuming the graph is y=-3(√2x)-4 and y=-3√(x-4) the transformation would be:

The graph is compressed horizontally by a factor of 2
x=1/2x'
y=-3(√2x)-4
y=-3(√x')-4

moved left 4
x=x'-4
y=-3(√x)-4
y=-3(√x'-4)-4

moved down 4
y=y'-4
y=-3(√x-4)-4
y'-4=-3(√x'-4)-4
y'=-3(√x'-4)-4 +4
y'=-3(√x'-4)

Answer: C. The graph is compressed horizontally by a factor of 2, moved left 4, and moved down 4.