Question

Function f(x) is represented on the graph. Which statement identifies the effect of replacing f(x) with 1/2f(x) on the graph? A)The curve would remain the same size but would be flipped upside down. B)The curve would remain the same size but would shift to the left. C)The curve would be narrower, but the vertex would be in the same position. D)The curve would be wider, but the vertex would be in the same position.

Answer 1

Answer:

Option (D)

Step-by-step explanation:

If a function f(x) is represented on a graph and we follow the transformation as,

f(x) → $k.f(x)$

1). If k ≥ 1, graph of the parent function f(x) will be stretched vertically by a factor k.

That means the transformed graph will be narrower.

2). If 0 < k < 1, graph will be vertically compressed or the transformed function will show a wider graph.

Following this rule,

f(x) → $\frac{1}{2}.f(x)$ shows k = $\frac{1}{2}$ [Since 0 < $\frac{1}{2}$ < 1]

Therefore, transformed form will be wider.

Option (D) will be the answer.