The function f(x) = x2 is translated 7 units to the left and 3 units down to form the function g(x). Which represents g(x)?
2 answers:
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Given:
The given functions are:
To find:
The transformations performed of f(x) to create g(x).
Solution:
The translation is defined as
.... (i)
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.
We have,
Using these two function, we get
...(ii)
On comparing (i) and (ii), we get
It means the graph of f(x) is vertically stretched with a scale factor of 3, shifts 5 units left and 2 units down to get g(x).
Therefore, the correct options are A and C.