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The graph of g (x) = x cubed minus x is shown.
On a coordinate plane, a cubed root function is shown. It approaches x = negative 2 in quadrant 3, has a point of inflection at (0, 0), and approaches x = 2 in quadrant 1. It crosses the x-axis at negative 1 and 1.
Which is the graph of 0.5 g (x minus 2) + 1?
On a coordinate plane, a cubic root function is shown. It approaches x = negative 3 in quadrant 3, has an inflection point at (negative 1, negative 2), and then approaches y = 2 in quadrant 1. It crosses the y-axis at (0, negative 2).
On a coordinate plane, a cubic root function is shown. It approaches x = negative 1 in quadrant 3, has an inflection point at (2, 1), and then increases and approaches y = 5.
On a coordinate plane, a cubic root function is shown. It approaches the y-axis in quadrant 4, increases, has a point of inflection at (2, 1), and then increases and approaches x = 4.
On a coordinate plane, a cubic root function is shown. It approaches the y-axis in quadrant 2, decreases, has a point of inflection at (negative 2, 1), and then decreases and approaches x = negative 4.

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Answer:

b

Step-by-step explanation:

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The graph of the transformations applied to the function g(x) can be seen at the end of the answer.

Which is the graph of the function 0.5*g(x - 2) + 1?

Here we have some transformations applied to the function g(x).

g(x) = x^3 - x

First, we start with g(x). Then we apply a vertical contraction of scale factor 0.5, so we get:

h(x) = 0.5*g(x).

Now we translate the function 1 unit upwards, so we get:

h(x) = 0.5*g(x) + 1

Finally, we move the graph 2 units to the right, so we get:

h(x) = 0.5*g(x - 2) + 1.

h(x) = 0.5*( (x - 2)^3 - (x - 2)) + 1

The graph of this function can be seen below.

If you want to learn more about transformations, you can read:

https://brainly.com/question/4289712

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