Transform the given function as described and and write the resulting function as an equation

Question

f(x)= √x

compress horizontally by a factor of 2

reflect across the Y axis

translate up 2 units

Answer 1

g(x) = -(1/2)x^(1/2) + 2

compression by factor of 2 means multiply f(x) by 1/2

reflect across y axis means change the sign from positive to negative

translate up by 2 means add 2

f(x) = sqrx

then sqrx/2

then -sqrx/2

then -sqrx/2 + 2

g(x) = -(1/2)x^(1/2) + 2

g(x) is the top half of a leftward opening parabola with vertex = (0,2) compressed horizontally by factor of 2 (same as stretched vertically by a factor of 2)

f(x) was the top half of a rightward opening parabola with vertex (0,0)