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Match each verbal description to its equivalent function rule as applied to the given function below.
f(x) = 70 + 5/(*) = 71 +5
g(
= 213 + 17
9(2)
= 14 + 79(1) = 141 +7
9(2)
73 + 149(*) = 75 + 14
9(2)
= – 7:– 169(1) = -71 – 16
9(30)
= 70
189(1) = 71 – 18
g(x)
- 720 + 169(3)
-75 + 16
The function f stretched vertically by a
factor of 2 and translated down by 3 units.
<
The function f translated
2 units down and 3 units right.

Match each verbal description to its equivalent function rule as applied to the given function below fx 70 5 71 5 g 213 17 92 14 791 141 7 92 73 149 75 14 92 7 class=

Respuesta :

sqdancefan

9514 1404 393

Answer:

  1. g(x) = 14x +7
  2. g(x) = 7x -18
  3. g(x) = -7x -16
  4. g(x) = 21x +17

Step-by-step explanation:

The transformations of interest here are ...

  • g(x) = b·f(x) . . . . vertical scaling by a factor of b
  • g(x) = f(-x) . . . . . reflection across the y-axis
  • g(x) = f(x -h) +k . . . translation h units right and k units up

1. The transformation parameters are given as b=2, (h, k) = (0, -3). Then we have ...

  f1(x) = 2f(x) = 2(7x +5) = 14x +10 . . . . . vertical stretch by 2

  g(x) = f1(x -0) -3 = 14(x -0) +10 -3

  g(x) = 14x +7

__

2. (h, k) = (3, -2)

  g(x) = f(x -3) -2 = 7(x -3) +5 -2 = 7x -21 +3

  g(x) = 7x -18

__

3. The reflection gives us ...

  f1(x) = f(-x) = 7(-x) +5 = -7x +5

Then the translation 3 left is (h, k) = (-3, 0).

  g(x) = f1(x -(-3)) +0 = -7(x +3) +5 = -7x -21 +5

  g(x) = -7x -16

__

4. The transformation parameters are b = 3 and (h, k) = (0, 2).

  f1(x) = 3f(x) = 3(7x +5) = 21x +15 . . . . . . vertical stretch by 3

  g(x) = f1(x) +2 = 21x +15 +2

  g(x) = 21x +17

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