The graph of g is a vertical shrink by a factor of 1/3 and a reflection in the y-axis, followed by a translation 3 units right of the graph of f(x)=x2. Write a rule for g.

Transformation involves changing the position of a function.

The rule for g is:

The parent function is given as:

The rule of vertical shrink by a factor of 1/3 is:

So, we have:

The rule of reflection across the y-axis is:

So, we have:

The rule of translation 3 units right is:

So, we have:

Hence, the rule for g is:

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g(x) = (1/3)*(-x)^2 + 3.

Step-by-step explanation:

Let's define all the transformations in a general way,

A vertical contraction/dilation of a scale factor a is written as:

g(x) = a*f(x)

where if a > 1, it is a dilation.

if  0 < a < 1, it is a contraction.

A reflection in the y-axis changes the value of the x-component and leaves the y-component invariable, then this transformation is written as:

g(x) = f(-x).

A translation of A units up (A positive) is written as:

g(x) = f(x) + A.

Then for this case we have:

A dilation with scale factor 1/3.

g(x) = (1/3)*f(x)

A reflection over the y-axis.

g(x) = (1/3)*f(-x)

A translation of 3 units up.

g(x) = (1/3)*f(-x) + 3

(in that order, remember that the order in which you applly the transformations matters)

Then g(x) = (1/3)*f(-x) + 3

and f(x) = x^2, so we can replace that in the equation for g(x)

g(x) = (1/3)*(-x)^2 + 3.

54.864 meters

step-by-step explanation: