Which statement correctly describes the relationship between the graph of f(x) and g(x)=f(x−3)?

the graph of g(x) is the graph of f(x) translated 3 units right.

the graph of g(x) is the graph of f(x) translated 3 units up.

the graph of g(x) is the graph of f(x) translated 3 units left.

the graph of g(x) is the graph of f(x) translated 3 units down.

The correct option is first, i.e.,The graph of g(x) is the graph of f(x) translated 3 units right.

Explanation:

The standard form of transformation can be defined as,

g(x)=f(x+a)+b   (1)

If a>0, then the graph of f(x) shifts left side by a unit and if If a<0, then the graph of f(x) shifts right side by a units.

If b>0, then the graph of f(x) shifts upward by b unit and if If a<0, then the graph of f(x) shifts downward by b units.

Since the relationship between the graph of f(x) and g(x) is,

g(x)=f(x−3)

Compare this with equation (1),

we can say that the value of a is -3, therefore the graph of f(x) translated 3 units right.

Therefore, the correct option is first.

i hope this is what you were looking for.

see attached graph

solve systems of equations by graphing. a system of linear equations contains two or more equations e.g. y=0.5x+2 and y=x-2. the solution of such a system is the ordered pair that is a solution to both equations. to solve a system of linear equations graphically we graph both equations in the same coordinate system