Answer:
The following functions would move the graph of the function to the right on the coordinate plane.
C) [tex]f(x-3)+1[/tex]
G) [tex]f(x-5)[/tex]
Step-by-step explanation:
We need to check for those functions which shows a horizontal shift of graph to the right.
Translation Rules:
Horizontal shift:
[tex]f(x)\rightarrow f(x+c)[/tex]
If [tex]c>0[/tex] the function shifts [tex]c[/tex] units to the left.
If [tex]c<0[/tex] the function shifts [tex]c[/tex] units to the right.
Vertical shift:
[tex]f(x)\rightarrow f(x)+c[/tex]
If [tex]c>0[/tex] the function shifts [tex]c[/tex] units to the up.
If [tex]c<0[/tex] the function shifts [tex]c[/tex] units to the down.
Applying rules to identify the translation occuring in each of the given functions.
A) [tex]f(x+2)-7[/tex]
Translation: [tex]f(x)\rightarrow f(x+2)-7[/tex]
The translation shows a shift of 2 units to the left and 7 units down.
B) [tex]f(x)-3[/tex]
Translation: [tex]f(x)\rightarrow f(x)-3[/tex]
The translation shows a shift of 3 units down.
C) [tex]f(x-3)+1[/tex]
Translation: [tex]f(x)\rightarrow f(x-3)+1[/tex]
The translation shows a shift of 3 units to the right and 1 units up.
D) [tex]f(x)+4[/tex]
Translation: [tex]f(x)\rightarrow f(x)+4[/tex]
The translation shows a shift of 4 units up.
F) [tex]f(x+6)[/tex]
Translation: [tex]f(x)\rightarrow f(x+6)[/tex]
The translation shows a shift of 6 units to the left.
G) [tex]f(x-5)[/tex]
Translation: [tex]f(x)\rightarrow f(x-5)[/tex]
The translation shows a shift of 5 units to the right.
