SOLUTION: Find the function f(x) = 1/x, Shift left 1 unit, shift up 3 units, reflect about the y-axis. I am completely lost with this question. Would someone please explain?

Algebra ->  Functions -> SOLUTION: Find the function f(x) = 1/x, Shift left 1 unit, shift up 3 units, reflect about the y-axis. I am completely lost with this question. Would someone please explain?       Log On


   

Question 536557: Find the function
f(x) = 1/x, Shift left 1 unit, shift up 3 units, reflect about the y-axis. I am completely lost with this question. Would someone please explain?

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Shift f(x) left 1 unit - What happens for f(x) at x=1, you want it to happen for your g(x) at x=0. You want g(0)=f(1). To do that you replace x with x+1 and g(x) = f(x+1)
Shift f(x) up 3 units - You just add 3 to the value of the function and g(x)= f(x)+3
Reflect about the y-axis - What happens for f(x) at any x value, you want it to happen at -x, at the same distance to the other side of the y-axis, so that g(x)=f(-x).
Shift left 1 unit - From f(x)=1/x, you change to s(x)=1/(x+1)
Shift up 3 units - From s(x)=1/(x+1), you change to u(x)=1/(x+1)+3
Reflect about the y-axis - From u(x)=1/(x+1)+3, you change to g(x)=1/((-x)+1)+3, more elegantly written as g(x)=1/(1-x)+3
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