contestada

Which function represents the exponential function f(x)=3x after a vertical stretch by a factor of 8 and a reflection across the x-axis?
A) g(x) =3-8x
B) g(x) =-3 8x
C) g(x) =8·3-x
D) g(x) =-8·3x

Respuesta :

AlbertThomas
-8×3x represents a vertical strech by a factor of
8 and a reflection across the x-axis.

The answer is D.

Using translation concepts, it is found that the function after a vertical stretch by a factor of 8 and a reflection across the x-axis is given by:

D. [tex]g(x) = -8(3)^x[/tex]

The given function is:

[tex]f(x) = 3^x[/tex]

What is a translation?

  • A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

A vertical stretch by a factor of 8 means that the function is multiplied by 8, so:

[tex]g(x) = 8(3)^x[/tex]

The reflection across the x-axis means that the function is multiplied by -1, hence:

[tex]g(x) = -8(3)^x[/tex]

Hence option D is correct.

You can learn more about translation concepts at https://brainly.com/question/4521517

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