Question

The graph of f (x)=√x is transformed to create the

graph of g (x)= -2√x+6. Which of these describes a
transformation used to create the graph of g?

Answer 1

The transformation used to create the graph of g(x) from the graph of f(x) is a vertical and horizontal transformation.

The "-2" in the equation of g(x) reflects a vertical stretch by a factor of 2, which causes the graph to become narrower and steeper than f(x).

The "+6" in the equation of g(x) reflects a vertical shift upward by 6 units, which moves the entire graph of g(x) upward by 6 units.

Therefore, the transformation used to create the graph of g(x) from the graph of f(x) is a vertical and horizontal transformation.