Question

How would you write this in written form as an equation?

Answer 1

Explanation

We are given the parent function:

`f(x)=\log_x`

First, the horizontal shift 6 spaces to the left follows the rule:

`f(x)\to f(x+6)`

Next, the vertical shift 2 spaces down follows the rule:

`\begin{gathered} f(x)\to f(x)-2 \\ f(x+6)\to f(x+6)-2 \end{gathered}`

Finally, the reflection over y = k can be represented as:

`\begin{gathered} Let\text{ }g(x)\text{ }be\text{ }the\text{ }combined\text{ }function \\ g(x)=2k+2-f(x+6) \\ \therefore g(x)=2k+2-log(x+6) \end{gathered}`

Suppose k = 2, the graph becomes:

The red curve is the reflected curve.

Hence, the answer is:

`\begin{equation*} g(x)=2k+2-log(x+6) \end{equation*}`