noahbrown12
contestada

Let the graph of g be a translation 3 units up, followed by a vertical stretch by a factor of 2 and a reflection in the x-
Axis of the graph of
f(x) =3x^2-3x write a rule for g


G(x) =

15 points!!!!

Respuesta :

osaremenuwaifo

Answer:

The answer is [tex]g(x)= -6x(x-1)+3[/tex]

Step-by-step explanation:

we know that f(x) is written as [tex]3x^{2}-3x[/tex]

to show that the graph is being translated up, vertically stretching, and reflecting across the x axis, we need to factor the function.

[tex]f(x)= 3x^{2}-3x \\ 3x(x-1)\\[/tex]

now we can incorporate the changes to this graph.

multiply 3x by 2 and -1. (2 for a stretch and -1 for a reflection).

[tex]-6x(x-1)[/tex]

tack on the +3 to show a translation of 3 units up.

[tex]-6x(x-1)+3[/tex]

therefore, [tex]g(x)= -6x(x-1)+3[/tex]

hope this helps!

adioabiola

The rule for the graph of g after all transformations of the function f(x) = 3x² -3x is;

g(x) = 6x² + 3x + 6

The graph of f(x) is given as;

f(x) =3x^2-3x

According to the parameters given;

First, the graph of g is a translation 3 units up, therefore, we have;

  • g(x) = f(x) + 3

  • g(x) = 3x² - 3x + 3

Secondly, followed by a vertical stretch by a factor of 2 and a reflection in the x axis.

This means that the graph must be multiplied by 2 and x values containing x be now regarded as -x

  • g(x) = 6x² - 3x + 6

And a reflection in the x-axis yields;

  • g(x) = 6(-x)² -3(-x) + 6

  • g(x) = 6x² + 3x + 6

Ultimately, the rule for the graph of g is;

g(x) = 6x² + 3x + 6.

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