Given :
The parent tangent function is horizontally compressed by a factor of 1/2 and reflected over the x-axis.
Explanation :
To find the equation of g.
The tangent function is
[tex]f(x)=\tan x[/tex]It is horizontally compressed by a factor of 1/2.
Then the function becomes
[tex]g(x)=\tan (\frac{1}{2}x)[/tex]After that it is reflected over x-axis.
[tex]g(x)=-\tan (\frac{1}{2}x)[/tex]Answer :
Hence the result of the transformation is
[tex]g(x)=-\tan (\frac{1}{2}x)[/tex]The correct option is D.