Answer :
Answer: 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.
Answer:
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:
[tex]g(x)=f(x-3)[/tex]
The general transformation of function is given by:
[tex]g(x) = f(x+a)+b[/tex]
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.