Describe how to transform the graph of g (x) = ln x into the graph of f (x) = ln (3-x) - 2.

The graph of g (x) = ㏑x translated 3 units to the right and then reflected

about the y-axis and then translated 2 units down to form the graph of

f (x) = ㏑ (3 - x) - 2

Step-by-step explanation:

* Lets talk about the transformation

- If the function f (x) reflected across the x-axis, then the new

function g (x) = - f (x)

- If the function f (x) reflected across the y-axis, then the new

function g (x) = f (-x)

- If the function f (x) translated horizontally to the right

by h units, then the new function g (x) = f (x - h)

- If the function f (x) translated horizontally to the left

by h units, then the new function g (x) = f (x + h)

- If the function f (x) translated vertically up

by k units, then the new function g (x) = f (x) + k

- If the function f (x) translated vertically down

by k units, then the new function g (x) = f (x) - k

* lets solve the problem

∵ Graph of g (x) = ㏑x is transformed into graph of f (x) = ㏑ (3 - x) - 2

- ㏑x becomes ㏑ (3 - x)

∵ ㏑ (3 - x) = ㏑ (-x + 3)

- Take (-) as a common factor

∴ ㏑ (-x + 3) = ㏑[ - (x - 3) ]

∵ x changed to x - 3

∴ The function g (x) translated 3 units to the right

∵ There is (-) out the bracket (x - 3) that means we change the sign

of x then we will reflect the function about the y-axis

∴ g (x) translated 3 units to the right and then reflected about the

y-axis

∵ g (x) changed to f (x) = ㏑ (3 - x) - 2

∵ We subtract 2 from g (x) after horizontal translation and reflection

about y-axis

∴ We translate g (x) 2 units down

∴ g (x) translated 3 units to the right and then reflected about the

y-axis and then translated 2 units down

* The graph of g (x) = ㏑x translated 3 units to the right and then

reflected about the y-axis and then translated 2 units down to

form the graph of f (x) = ㏑ (3 - x) - 2

c edge