[tex]k\bullet f(x)[/tex] will stretch the [tex]f(x)=4^x[/tex] vertically by a factor of k, if [tex]k\:>\:0[/tex], but if [tex]0\:<\:k\:<\:1[/tex] the graph will shrink vertically by a factor of k.
Part B.
[tex]f(x+k)[/tex] is a horizontal transformation, that moves the graph of the function h units to the left.
Part C
[tex]f(x)+k[/tex] shifts the function up vertically by k units.
Part D
Given
[tex]f(x)=4^x[/tex] as the parent function,
i) [tex]f(x-2)[/tex] shifts [tex]f(x)=4^x[/tex], 2 units to the right.
ii)[tex]f(x)+2[/tex] shifts the graph 2 units up.
iii) [tex]3f(x)[/tex] stretches [tex]f(x)=4^x[/tex] vertically by a factor of 2 units.
iv) [tex]4^{x+4}=f(x+4)[/tex] which shifts the function horizontally 4 units to the left