Question

HELP PLEASE!!!Describe the change in the graph of the parabola f(x) when it transforms into g(x) =1/2f(x)

The parabola g(x) will open in the opposite direction of f(x), and the parabola will be narrower than f(x).

The parabola g(x) will open in the same direction of f(x), and the parabola will be narrower than f(x).

The parabola g(x) will open in the opposite direction of f(x), and the parabola will be wider than f(x).

The parabola g(x) will open in the same direction of f(x), and the parabola will be wider than f(x).

Answer 1

Last one:

The parabola g(x) will open in the same direction of f(x), and the parabola will be wider than f(x).

Explanation:

g(x) = ½f(x)

g(x) is obtained by a vertical stretch of f(x) by factor ½ (compression)

g(x) would look like f(x), would just be wider

Answer 2

D

Explanation:

These are transformations. One thing to remember is that only a sign change (like a negative sign on the new function) will change the direction in which the parabola opens.

Here, going from f(x) to 1/2 * f(x) has no sign change, so the parabola will open in the same direction as before. Eliminate A and C.

Vertical transformations are those that are done to the entire function, as opposed to horizontal transformations which are done only on the x. Here, since we're multiplying 1/2 to f(x), we have a vertical transformation.

There are different transformations. The one here would be a vertical shrink by a factor of 1/2. Vertically shrinking a function is basically the same as compressing it, which would make it wider.

The answer is thus D.