How do you graph y=2-sqrt(x-2)?

1 Answer
Bill K. ยท Adrian D.
Jul 30, 2015

Take the graph of y=sqrt(x), shift (translate) it to the right by 2 units, reflect it across the x-axis, then shift (translate) it up by 2 units.

Explanation:

Given a function g(x), to get the graph of y=g(x-2) you should shift the graph of y=g(x) to the right by 2 units. Then to get the graph of y=-g(x-2) you should reflect the graph of y=g(x-2) across the x-axis. Finally, to get the graph of y=2-g(x-2) you should shift the graph of y=-g(x-2) up by 2 units.

You can also plot some points to help. Let f(x)=2-sqrt{x-2}. Then f(2)=2-sqrt{0}=2, f(3)=2-sqrt{1}=1, f(4)=2-sqrt{2} approx 0.59, f(5)=2-sqrt{3} approx 0.27, f(6)=2-sqrt{4}=0, f(7)=2-sqrt{5} approx -0.24, etc...

graph{2-sqrt(x-2) [-1, 10, -2.5, 2.5]}

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