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Line m is represented by the function f(x) = 1/3x +5/2. After transformation, the image, line m’, is represented by the functions g(x) = 1/2 f(x+3) + 1/2. Which statements below describe the transformation from m to m’? Select all that apply.

A.) m is dilated by a scale factor of 1/3

B.) m is shifted to the left 3 units

C.) m is shifted to the left 5/2 units

D.) m is shifted up 1/2 units

E.) m is dilated by a factor of 2

Respuesta :

tramserran

Answer:  B)  left 3 units

Step-by-step explanation:

The vertex form of a quadratic function is: f(x) = a(x - h)² + k    where;

  • a represents the vertical stretch
  • h represents the x-coordinate of the vertex
  • k represent the x-coordinate of the vertex

the change from f(x) to g(x) is:

  • the a-value is multiplied by 1.5
  • the h-value (x-coordinate) is -3
  • the k-value is decreased by 2

This results is:

  • vertical stretch by a factor of 1.5
  • shift to the left 3 units      (this is option B!)
  • shift down 2 units

The line m', which represented the function after transformation of line m is shifted to the left 3 units. Thus the option B is correct option.

What is the dilation of function?

Dilation of a function is means to the transformation of the function. The factor by which the given function is dilated, called the scale factor of dilation.

Let a function is f(x) then, [tex]a[/tex]f(x) represent the dilation of function with a units vertically.

Types of shifting of function-

  • Horizontal shift- Let the parent function is f(x). Thus by replacing parent function with f(x-b) shifts the graph b units right and by replacing parent function with f(x+b) shifts the graph b units left.
  • Vertical shift- Let the parent function is f(x). Thus by replacing parent function with f(x)-c shifts the graph c units down and by replacing parent function with f(x)+c shifts the graph c units up.

Given information-

The function represented by the line m is,

[tex]f(x) = \dfrac{1}{3}x +\dfrac{5}{2}[/tex]

The function represented by the line m' is,

[tex]g(x) = \dfrac{1}{2}\times f(x+3) +\dfrac{1}{2}[/tex]

Here in the given equation the function is multiplied with unit 1/2, the graph the scale factor of it should be 1/2.

As the function is added with 3 units, thus the graph is shifted 3 units left.

As the unit 2 is subtracted from the given function. Thus the graph shifted 2 units down.

Thus, the correct option is, m is shifted to the left 3 units. Hence, the option B is the correct option.

Learn more about the dilation of function here;

https://brainly.com/question/15706158

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