Answer:
Option c. Reflection across the x-axis and vertical stretch by a factor of 7
Step-by-step explanation:
If the graph of the function [tex]y = cf(x)[/tex] represents the transformations made to the graph of [tex]y = f(x)[/tex] then, by definition:
If [tex]0 <c <1[/tex] then the graph is compressed vertically by a factor a.
If [tex]|c| > 1[/tex] then the graph is stretched vertically by a factor a.
If [tex]c <0[/tex] then the graph is reflected on the x axis.
In this problem we have the function [tex]y = -7secx[/tex] and our paretn function is [tex]y = secx[/tex]
therefore it is true that
[tex]c = -7\\\\|-7|> 1\\\\-7 <0[/tex].
Therefore the graph of [tex]y = secx[/tex] is stretched vertically by a factor of 7 and is reflected on the x-axis
Finally the answer is Option c
