hELP WITH A pRECALC QUESTION?

Question

if Y= I X-2 l +3, then give the equation for the graph when rotated 90 deg. clockwise about the origin.

Please tell me your work and how you got to the answer this is the last problem on my homework I am really stumped thank you SOOOO much

Answer 1

First find a piecewise function for y = f(x) that doesn't involve the absolute value sign.

y = x - 2 + 3 = x + 1 for x ≥ 2
y = -x + 2 + 3 = -x + 5 for x < 2

y = x + 1 for x ≥ 2
y = -x + 5 for x < 2

If you rotate it 90° it becomes a function of y. x = g(x). Graph it and you will get an idea.

y = x + 1 for x ≥ 2 becomes
x = y - 1 for y ≥ 3

y = -x + 5 for x < 2 becomes
x = -y + 5 for y < 3

x = y - 1 for y ≥ 3
x = -y + 5 for y < 3

or

x = | y - 3 | + 2