Write the equation g(x) of the transformation of the parent graph f(x) = |x| stretched vertically by a factor of 2, reflected over the x-axis, and translated left 1 unit and down 3 units.

g(x) = -2|x+1| -3

Step-by-step explanation:

f(x) = |x|

y = f(x) + C C < 0 moves it down

y = |x| -3  for  shifting down 3

y = f(x + C)C > 0 moves it left

y = |x+1| -3 for move it left 1

y = Cf(x)  C > 1 stretches it in the y-direction

y = 2|x+1| -3 to stretch it 2 vertically

y = −f(x)  Reflects it about x-axis

y = -2|x+1| -3

We start off with f(x) = |x|

c < 0 means move down

y = f(x) + c

3 units down

After: y = |x| - 3

c > 0 means move left

y = f(x + c)

1 unit left

After: y = |x + 1| - 3

c > 1 means y direction stretch

y = cf(x)

2 unit stretch

After: y = 2|x + 1| - 3

Reflect across x-axis can be stated as y = -f(x)

After: y = -2|x + 1| - 3

Best of Luck!

step-by-step explanation:

for exempl this   system of equations   y = x - 3

                                                                y = 2x - 5

look   the line : y = x -3     ( red)

                            the line : y = 2x -5 ( bleus)

the value of x is 9 ⇒ answer b

step-by-step explanation:

* we can solve this problem using cosine and sine rule

- in δ abc

∵ ab = 36 , bc = 28 , ac = 16

- lets find the measure of angle b using the cosine rule

∵ cos b = [ab² + bc² - ac²]/2(ab)(bc)

∴ cos b = [36² + 28² - 16²]/2(36)(28)

∴ cos b = 19/21

∴ m∠b = cos^-1(19/21) ≅ 25°

- lets find the measure of angle a using the sine rule

∵ sina/bc = sinb/ac = sinc/ab

∴ sina/28 = sin25°/16 ⇒ by using cross multiplication

∴ sina = 28 × sin25°/16

∴ sina = 0.7396

∴ m∠a = sin^-1(0.7396) ≅ 48°

- from the figure m∠abd = m∠dbc

∵ m∠abc = 25°

∴ m∠abd = 25°/2 = 12.5°

- in δabd

∵ m∠a = 48° , m∠abd = 12.5°

∵ the sum of the measures of the interior angles of any δ is 180°

∴ m∠adb = 180° - (48° + 12.5°) = 119.5°

∵ ab = 36

∵ ad = x

- use the sine rule to find x

∵ sin∠adb/ab = sin∠abd/x

∴ sin119.5°/36 = sin12.5°/x ⇒ by using cross multiplication

∴ x = 36 × sin12.5°/sin119.5° = 8.95 ≅ 9

* the value of x is 9