f(x)=\sqrt(x); reflect in the y-axis, shrink vertically by a factor of (1)/(2) and shift upward 2 units.

Question

A function is given, and the indicated transformations are applied to its graph (in the given order). Write the equation for the final graph.

Answer 1

So the parent function is f(x) = √x.

Here are the transformations and corresponding changes in the equations:

1. Reflect over the y-axis. (Add a negative sign in front of x, inside the radical sign)

f(x) = √-x

2. Shrink vertically by 1/2. Multiply the equation by 1/2

f(x) = (1/2) √-x

3. Shift up 2. Add 2, OUTSIDE the radical sign. Adding 2 INSIDE the radical sign means to shift left.

f(x) = (1/2) √-x + 2

Answer 2

f₁(x) = -√x

f₂(x) = -(1/2)√x

f₃(x) = (-(1/2)√x) + 2