Which statement correctly describes the relationship between the graph of f(x) and g(x)=f(x+2) ?

The graph of g(x) is the graph of f(x) translated 2 units down.

The graph of g(x) is the graph of f(x) translated 2 units right.

The graph of g(x) is the graph of f(x) translated 2 units up.

The graph of g(x) is the graph of f(x) translated 2 units left.

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musiclover10045 musiclover10045 · Answer 1 · 2019-10-10T18:35:19+02:00

Adding a value to the X value shifts the graph that many units to the left.

X+2 adds 2 to x, so the graph would shift 2 unites to the left.

The answer is:

The graph of g(x) is the graph of f(x) translated 2 units left.

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erinna erinna · Answer 2 · 2019-10-24T11:26:45+02:00

Answer:

Option D.

Step-by-step explanation:

The transformation of a function is defined as

[tex]g(x)=kf(x+a)+b[/tex] .... (1)

Where, k is stretch factor, a is horizontal shift and b is vertical shift.

If 0<k<1, then the graph compressed vertically by factor k and if k>1, then the graph stretch vertically by factor k.

If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.

If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.

The given relationship between two function is

[tex]g(x)=f(x+2)[/tex] .... (2)

On comparing (1) and (2) we get

h=2> 0, so the graph of g(x) is the graph of f(x) translated 2 units left.

Therefore, the correct option is D.