Question

Beginning with the graph of f(x) = x^2, what is the transformations are needed to form g(x) = 1/2(x+4)^2-3

A. The graph of g(x) is narrower than f(x) and is shifted to the right 4 units and down 3 units.
B. The graph of g(x) is narrower than f(x) and is shifted to the left 4 units and down 3 units.
C. The graph of g(x) is wider than f(x) and is shifted to the left 4 units an down 3 units.
D. The graph of g(x) is wider than f(x) and is shifted to the right 4 units and down 3 units.

Answer 1

C. The graph of g(x) is wider than f(x) and is shifted to the left 4 units and down 3 units.

Explanation:

You want to know the transformations needed to form g(x) = 1/2(x+4)^2 -3 from f(x) = x^2.

Transformations

The transformations ...

f(x) ⇒ g(x) = c·f(x -h) +k

represent vertical expansion by a factor of 'c', right shift by 'h' units, and an upward shift of 'k' units.

Application

Here, we have c=1/2, h=-4, k=-3. These mean the function f(x) has been vertically compressed to 1/2 its original height, and shifted left 4 and down 3.

The vertical compression will cause the graph to appear to be wider for any given distance above the vertex.