Question

Question is in image

Answer 1

The given function is,

`f(x)=x`

If the graph of a function f(x) is shifted k units horizontally to the left or to the right, then the new function g(x) is,

`g(x)=f(x-k)`

If k>0, the graph is shifted to the right.

If k<0, the graph is shifted to the left

Since f(x) is shifted 13 units to the left, then k=-13.

Since f(x)=x, the shifting of f(x) by 13 units to the left gives g(x) as,

`\begin{gathered} g(x)=f(x-(-13)) \\ =f(x+13) \\ =x+13 \end{gathered}`

Therefore, the equation of the new function g(x)=x+13.