Answer:
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
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