Given:
The functions are:
[tex]h(x)=x^2[/tex]
[tex]k(x)=-\dfrac{1}{7}x^2[/tex]
To find:
The transformation from the graph of h to the graph of k.
Solution:
The transformation is defined as
[tex]k(x)=ah(x+a)=[/tex] Â Â Â Â Â Â Â Â .... (1)
Where, a is stretch factor
If 0<|a|<1, then the graph compressed vertically by factor |a| and if |a|>1, then the graph stretch vertically by factor |a|.
If [tex]a<0[/tex], then the graph of h(x) reflected across the x-axis.
We have,
[tex]h(x)=x^2[/tex]
[tex]k(x)=-\dfrac{1}{7}x^2[/tex]
It can be written as
[tex]k(x)=-\dfrac{1}{7}h(x)[/tex] Â Â Â Â ...(2)
On comparing (1) and (2), we get
[tex]a=-\dfrac{1}{7}<0[/tex]
The graph of h(x) reflected across the x-axis.
[tex]|a|=\dfrac{1}{7}<1[/tex]
So, the graph is compressed vertically.
It means the graph of h reflection over the x-axls and a vertical stretch to get the graph of k.
Therefore, the correct option is B.
