Question

Given the function f(x)=log5 x which of the following functions is the transformation of f(x) right 6 units up 3 units stretched vertically by a factor of 2 and reflected across the x axis
All my answers start with g(x)

Answer 1

To transform the function \( f(x) = \log_5 x \) according to the given transformations, we can apply each transformation step by step:

1. **Right 6 units**: We replace \( x \) with \( x - 6 \) in the function, giving us:
\[
f(x - 6) = \log_5(x - 6)
\]

2. **Up 3 units**: We add 3 to the entire function:
\[
f(x - 6) + 3 = \log_5(x - 6) + 3
\]

3. **Stretched vertically by a factor of 2**: We multiply the function by 2:
\[
2(\log_5(x - 6) + 3) = 2\log_5(x - 6) + 6
\]

4. **Reflected across the x-axis**: We multiply the entire function by -1:
\[
-[2\log_5(x - 6) + 6] = -2\log_5(x - 6) - 6
\]

Putting it all together, the transformed function is:
\[
g(x) = -2\log_5(x - 6) - 6
\]

So, the function \( g(x) \) representing the transformation of \( f(x) \) is:
\[
g(x) = -2\log_5(x - 6) - 6
\]