SOLUTION: Can someone show me how this is done, have a bunch of home work ? just like this one. The graph of f(x) = √x is horizontally stretched by a factor of 0.5, reflected in the

Algebra ->  Graphs -> SOLUTION: Can someone show me how this is done, have a bunch of home work ? just like this one. The graph of f(x) = √x is horizontally stretched by a factor of 0.5, reflected in the       Log On


   

Question 937573: Can someone show me how this is done, have a bunch of home work ? just like this one.
The graph of f(x) = √x is horizontally stretched by a
factor of 0.5, reflected in the y axis, and shifted two units
to the left.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
?
y%5E2=x

Stretch by factor of 0.5 is not stretch but shrink.
HORIZONTAL "stretch" is 0.5y%5E2=x, and you are interested in the upper branch.

Reflect in the y-axis,
-%281%2F2%29y%5E2=x

Shift two units to the left,
-%281%2F2%29y%5E2=x%2B2

Simplify this back into y as a function of x.
y%5E2=-2x-4
highlight%28y=sqrt%28-2x-4%29%29
This is the upper branch of the function.
Clearly understand that the expression within the square root function is NOT a negative value. You have a domain which relies on -2x-4%3E=0,
-4%3E=2x
-2%3E=x------the domain.

Aside from that, you can still adjust the equation as y=sqrt%28%28-2%29%28x%2B2%29%29.