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

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)`

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<0` 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<0` 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.