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!

597

step-by-step explanation:

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.