Question

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.

Answer 1

Option A) The graph of g(x) is the graph of ​f(x) translated 3 units right.

Step-by-step explanation:

We are given a relationship between two functions:

`g(x)=f(x-3)`

The general transformation of function is given by:

`g(x) = f(x+a)+b`

where a and b are constants.

a helps us to understand the translation that is the right and left movement in graph whereas b helps us to understand the upward and downward movement of the graph.

• If a > 0 and b > 0, then the graph of g(x) is translated to a units in the right and move upward by b units.

• If a < 0 and b > 0, then the graph of g(x) is translated to a units in the left and move upward by b units.

• If a > 0 and b < 0, then the graph of g(x) is translated to a units in the right and move downwards by b units.

• If a < 0 and b < 0, then the graph of g(x) is translated to a units in the left and move downward by b units.

Comparing the given relation with the general transformation, we get a = -3 and b = 0.

Thus, the graph of g(x) translates 3 units to the right.

Option A) The graph of g(x) is the graph of ​f(x) translated 3 units right.

Answer 2

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

Step-by-step 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.