Describe the transformation required to obtain the graph of the given function from the basic trigonometric graph.
y=-1 tan 1/10 x+4

Reflection across x-axis, horizontal stretch by a factor of 10

and vertical translation up 4 units ⇒ answer (c)

Step-by-step explanation:

* The basic function of tanФ is

# y = tanФ

1- If y = -tanФ ⇒ reflect y over the x-axis

2- If y = tan(-Ф) ⇒ reflect y over the y-axis

3- If y = tan(Ф - k) ⇒ shift y right k units

4- If y = tan(Ф + k) ⇒ shift y left k units

5- If y = tanФ + k ⇒ shift y up k units

6- If y = tanФ - k ⇒ shift y down k units

7- If y = k tanФ ⇒ multiply y-values by k

 (k > 1 stretch, 0 < k < 1 compressed vertical)

 The scale factor is k

8- If y = tan(kФ) ⇒ divide x-values by k

 (k > 1 compressed, 0 < k < 1 stretch horizontal)

 The scale factor is 1/k

* Lets solve the problem

∵ y = -tan(1/10)x + 4

* We will use rules number 1 , 5 and 8

∴ Reflect y over the x-axis, shift y up k units and stretch

   horizontal by scale factor is 1/k (0 < k < 1)

∴ Reflection across x-axis, horizontal stretch by a factor of 10

  and vertical translation up 4 units

part a: 1.08

part b: 27.59