Question

The graph of a function, ƒ( x), is plotted on the coordinate plane. Select two of the following functions that would move the graph of the function to the right on the coordinate plane.
A. ƒ( x + 2) – 7
B. ƒ( x) – 3
C. ƒ( x – 3) + 1
D. ƒ( x) + 4
F. ƒ( x + 6)
G. ƒ( x – 5)

Answer 1

Answer:

The following functions would move the graph of the function to the right on the coordinate plane.

C) $f(x-3)+1$

G) $f(x-5)$

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:

$f(x)\rightarrow f(x+c)$

If $c>0$ the function shifts $c$ units to the left.

If $c$ the function shifts $c$ units to the right.

Vertical shift:

$f(x)\rightarrow f(x)+c$

If $c>0$ the function shifts $c$ units to the up.

If $c$ the function shifts $c$ units to the down.

Applying rules to identify the translation occuring in each of the given functions.

A) $f(x+2)-7$

Translation: $f(x)\rightarrow f(x+2)-7$

The translation shows a shift of 2 units to the left and 7 units down.

B) $f(x)-3$

Translation: $f(x)\rightarrow f(x)-3$

The translation shows a shift of 3 units down.

C) $f(x-3)+1$

Translation: $f(x)\rightarrow f(x-3)+1$

The translation shows a shift of 3 units to the right and 1 units up.

D) $f(x)+4$

Translation: $f(x)\rightarrow f(x)+4$

The translation shows a shift of 4 units up.

F) $f(x+6)$

Translation: $f(x)\rightarrow f(x+6)$

The translation shows a shift of 6 units to the left.

G) $f(x-5)$

Translation: $f(x)\rightarrow f(x-5)$

The translation shows a shift of 5 units to the right.