Let the graph of g be a translation 2 units left and 3 units up, followed by a reflection in the y-axis of the graph of f(1) = ? - 24 Write a rule for g.

Answer:

g(x) = (x+2)^2 - 2x - 1

Step-by-step explanation:

f(x) = x^2 - 2x

g(x) = f(x+2) + 3

g(x) = (x+2)^2 -2(x+2) + 3 = (x+2)^2 - 2x - 1

When we graph the equations, we can confirm that our answer is correct.

The required solution of the given function is  f(x) =[tex]x^{2} -2x[/tex] is reflection on y axis is [tex]g(x)= (x+2)^2 - 2x - 1[/tex].

A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure. The original shape of the object is called the Pre-Image and the final shape and position of the object is the Image under the transformation.

Given:

The given function is

f(x) =[tex]x^{2} -2x[/tex]

According to given question we have

[tex]g(x) = (x+2)^2 - 2x - 1[/tex]

The graph of g be a translation 2 units left and 3 units up, followed by a reflection in the y-axis of the graph.

By the use reflection on y axis we get

[tex]f(x) = x^2 - 2x\\g(x) = f(x+2) + 3\\g(x) = (x+2)^2 -2(x+2) + 3\\ \\g(x)= (x+2)^2 - 2x - 1[/tex]

Therefore, the required solution of the given function is  f(x) =[tex]x^{2} -2x[/tex] is reflection on y axis is [tex]g(x)= (x+2)^2 - 2x - 1[/tex].

Learn more details about transformations here:

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Public Colleges
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