Question

The graph of f(x) is transformed into the graph of g(x), such that g(x) = k ⋅ f(x).

graph of the function of f of x is a downward opening parabola with vertex at the origin and the graph of g of x a downward opening parabola with vertex at the origin with a narrower opening than f of x

Which of the statement describes the transformation?

a
The graph of g(x) is a vertical shrink of the graph of f(x), with the k between −1 and 0.

b
The graph of g(x) is a vertical shrink of the graph of f(x), with the k value between 0 and 1.

c
The graph of g(x) is a vertical stretch of the graph of f(x), with the k value greater than 1.

d
The graph of g(x) is a vertical stretch of the graph of f(x), with the k value less than −1.

Answer 1

The statement that describes the transformation is:

c) The graph of g(x) is a vertical stretch of the graph of f(x), with the k value greater than 1.

In the given scenario, the graph of f(x) is a downward opening parabola with the vertex at the origin. When the graph is transformed into g(x), which is described as a downward opening parabola with a narrower opening than f(x), it implies that the graph of g(x) has been vertically stretched. This means that the k value in the equation g(x) = k ⋅ f(x) is greater than 1, indicating a vertical stretch.

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