Describe the transformation required to obtain the graph of the given function from the basic trigonometric graph.
-$$y = - \tan \frac { 1 } { 9 } x + 7$$
A) Reflection across the $x$-axis, horizontal shrink by a factor of $\frac { 1 } { 9 }$, and vertical translation down 7 units.
B) Horizontal stretch by a factor of 9 and a vertical translation up 7 units.
C) Reflection across the $x$-axis, horizontal translation to the right 9 units, and vertical translation up 7 units.
D) Reflection across the x-axis, horizontal stretch by a factor of 9 , and vertical translation up 7 units.

Question

Quizplus · Accepted Answer

The function $y = - \tan \frac { 1 } { 9 } x + 7$ involves a reflection across the x-axis due to the negative sign in front of the tangent function, a horizontal stretch by a factor of 9 because the coefficient inside the tangent function is $\frac{1}{9}$ (which inversely affects the period of the tangent function, thus stretching it), and a vertical translation up 7 units indicated by the "+7" outside the function.

Describe the Transformation Required to Obtain the Graph of the Given