Given:
The linear parent function is
[tex]f(x)=x[/tex]
To find:
The new function after vertical stretch by a factor of 4 and flip over the x-axis.
Solution:
The transformation is defined as
[tex]g(x)=kf(x)[/tex] .... (i)
Where, k is either vertical stretch or vertical compression.
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 k<0, then the graph flip over the x-axis.
It is given that the graph of f(x) vertically stretch by a factor of 4. So, |k|=4.
The graph flip over the x-axis. So, the value of k must be negative, i.e., k=4.
Using (i), we get
[tex]g(x)=-4f(x)[/tex]
We have, [tex]f(x)=x[/tex]
[tex]g(x)=-4x[/tex]
Therefore, the correct option is B.
