Answer:
Option c
Step-by-step explanation:
If the graph of the function [tex]y=cf(hx) +b[/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 c.
If [tex]|c| > 1[/tex] then the graph is stretched vertically by a factor c
If [tex]c <0[/tex] then the graph is reflected on the x axis.
If [tex]b> 0[/tex] the graph moves vertically upwards.
If [tex]b <0[/tex] the graph moves vertically down
If [tex]0 <h <1[/tex] the graph is stretched horizontally by a factor [tex]\frac{1}{h}[/tex]
If [tex]h> 1[/tex] the graph is compressed horizontally by a factor [tex]\frac{1}{h}[/tex]
In this problem we have the function [tex]y=-tan(\frac{1}{10}x) +4[/tex] and our parent function is [tex]y = tanx[/tex]
therefore it is true that [tex]c =-1<0[/tex] and [tex]b =4 > 0[/tex] and [tex]h=\frac{1}{10} ,\ \ 0<h<1[/tex]
Therefore the graph of [tex]y=tanx[/tex] is stretched horizontally by a factor of 10. Also as [tex]c=-1<0[/tex] is reflected on the x axis. Also, as b = 4> 0 then the graph moves vertically 4 units up
The answer is "Reflection across the x-axis, horizontal stretch by a factor of 10 and vertical translation up 4 units"
