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

false

step-by-step explanation:

4y - 6 + 4y^2 - 9

before simplifying this contains 4 terms

after simplifying

4y -15 + 4y^2

it contains 3 terms

(- 1, 0 )

step-by-step explanation:

an x- intercept is where the function crosses the x- axis.

to find the x- intercept/s look for the value of x when f(x) = 0

from the given table there are 3 values of x where f(x) = 0

when x = - 1, x = 2, x = 3

the one that is listed is (- 1, 0 )