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Match each verbal description to its equivalent function rule as applied to the given function below. 3a – 7 = 6 - 9 = -3.1 14 (1) و = 3x - 7 = 121 – 19 = 60 - 2 = -31 28 The function fstretched vertically by a factor of 4 and translated up by 9 units The function ftranslated 6 units up and 2 units right The function freflected about the y-axis and translated 7 units left The function f stretched vertically by a factor of 2 and translated up by 5 units​

Match each verbal description to its equivalent function rule as applied to the given function below 3a 7 6 9 31 14 1 و 3x 7 121 19 60 2 31 28 The function fstr class=

Respuesta :

Answer:f(x) = 3x - 7

6 up; 2 right = 3(x-2) - 7 + 6

= 3x - 6 - 7 + 6

= 3x - 7

reflected about y-axis; 7 left = -3(x+7) -7

= -3x - 21 - 7

= -3x - 28

up 5 ; 2 vert stretch = (2)(3x - 7) + 5

= 6x - 14 + 5

= 6x - 9

up 9 ; 4 vert stretch = (4)(3x - 7) + 9

= 12x - 28 + 9

= 12x - 19

Step-by-step explanation:

The transformation of a function may involve any change. The function f(x) stretched vertically by a factor of 2 and translated up by 5 units is (6x - 9).

How does the transformation of a function happen?

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs) etc.

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

  • Left shift by c units, y=f(x+c) (same output, but c units earlier)
  • Right shift by c units, y=f(x-c)(same output, but c units late)

Vertical shift:

  • Up by d units: y = f(x) + d
  • Down by d units: y = f(x) - d

Stretching:

  • Vertical stretch by a factor k: y = k × f(x)
  • Horizontal stretch by a factor k: y = f(x/k)

Given the function f(x)=3x-7, which can be transformed as shown below.

1. The function f(x) stretched vertically by a factor of 4 and translated up by 9 units.

Vertical stretch → 4(3x - 7) = 12x - 28

Up by 9 Units →  (12x - 28) + 9

g(x) = 12x - 19

2. The function f(x) translated 6 units up and 2 units right

Up by 6 units → (3x - 7) +6 = 3x - 1

2 units Right → 3(x-2) - 1 = 3x - 6 - 1 = 3x - 7

g(x) = 3x - 7

3. The function f(x) reflected about the y-axis and translated 7 units left

Reflected about the y-axis → -3x - 7

7 units left → -3(x+7) - 7 = -3x - 21 -7 = -3x-28

g(x) = -3x-28

4. The function f(x) stretched vertically by a factor of 2 and translated up by 5 units

Stretched vertically by a factor of 2 → 2(3x - 7) = 6x - 14

Translated up by 5 units → 6x - 14 + 5 = 6x - 9

g(x) = 6x - 9

Learn more about Transforming functions here:

https://brainly.com/question/17006186

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