We have the function f
[tex]f(x)=2^{x+4}+2[/tex]
And the function g
[tex]g(x)=2^{x-1}+6[/tex]
We can see two major differences, one is in the exponent and one in the constant term, but before talking about them, let's see how operations change the graph, consider a function h(x):
• h(x) + c, shift the graph of h(x) ,up ,"c" units
,
• h(x) - c, shift the graph of h(x) ,down, "c" units
,
• h(x + a), shift the graph of h(x) ,left ,"a" units
,
• h(x - a), shift the graph of h(x) ,right, "a" units
Then, we want to find out the relations between f and g.
Looking at the exponent we can see that the exponent of g is the exponent of f but subtracted 5, see that
[tex](x+4)-5=x-1[/tex]
And on the constant term, we have a difference of 4 positive, then we must add 4 to the function f to get g
Putting that all together, look that
[tex]\begin{gathered} f(x-5)+4=g(x)_{} \\ \\ 2^{(x-5)+4}+2+4=2^{x-1}+6 \end{gathered}[/tex]
Then, the function g is just f shifted 5 units to the right, and 4 units up
