Given f(x) and g(x) = f(x + k), use the graph to determine the value of k.6-3-63

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]