Answer:
[tex]g(x)=f(x+6)[/tex]
[tex]k=6[/tex]
Step-by-step explanation:
Given:
[tex]g(x)=f(x+k)[/tex]
Function transformation rule used:
[tex]g(x)=f(x+k)[/tex]
If value of [tex]k>1[/tex] then the graph shifts [tex]k[/tex] units to the left.
If value of [tex]k<1[/tex] then the graph shifts [tex]k[/tex] units to the right.
From the graph, it is clear that the function [tex]g(x)[/tex] has moved 6 units(-4 to-10) to the left of [tex]f(x)[/tex]. This shows that the value of [tex]k>1[/tex] and it is [tex]=6\ units[/tex]
Thus the transformation rule can be given as:
[tex]g(x)=f(x+6)[/tex]
∴ [tex]k=6[/tex]
