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.

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.

Option D.

Step-by-step explanation:

The transformation of a function is defined as

               .... (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

           .... (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.

the distance from any point on the parabola to the focus is the exact same as the distance from that point to the directrix.

if you could provide answer choices that might allow me to answer the question easier if my above answer isn't an option! (:

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