How do you graph y = 2\sqrt{2x+3}+1y=22x+3+1?

1 Answer
Oct 29, 2014

y=2sqrt{2x+3}+1y=22x+3+1

by factoring out 22,

Rightarrow y=2sqrt{2(x+3/2)}+1y=22(x+32)+1

by pulling sqrt{2}2 out,

Rightarrow y=2sqrt{2}sqrt{x+3/2}+1y=22x+32+1

Now, let us sketch y=sqrt{x}y=x, which looks like:

enter image source here

By stretching vertically by a factor of 2sqrt{2]22, we have y=2sqrt{2}sqrt{x}y=22x, which looks like:

enter image source here

By shifting left by 3/232, we have y=2sqrt{2}sqrt{x+3/2}y=22x+32, which looks like:

enter image source here

By shifting up by 1 unit, we have y=2sqrt{2}sqrt{x+3/2}+1y=22x+32+1, which looks like:

enter image source here

Above is the graph of y=2sqrt{2x+3}+1y=22x+3+1.


I hope that this was helpful.