What is the equation of the following graph?

1. f(x) = tan x-2
2. f(x) = tan x + 2
3. f(x) = 2tan x
4. f(x) = tan x -3

The required function is F(x) = tanx - 2.

Step-by-step explanation:

We all know the graph of tanx ,

The graph of tanx passes through the origin and repeats in the interval of π.

Now , after looking into the graph we can clearly say that it is the shifted graph of tanx , Which is shifted in the -y direction .

Thus ,

It is clear that F(x) must be like F(x) = tanx - c , where c is a positive constant .

Also, At x = 0 , Value of the function is coming out to be -2 ,

Putting x = 0 in F(x) = tanx - c , we get , F(x) = -c .

Thus c = 2.

So, the required function is F(x) = tanx - 2.

(a) x = 30°

(b) mRS =  30°

mST =  120°

mTU  = 120°

mUR = 90°

Step-by-step explanation:

(a) In the picture attached, the diagram is shown.

Given that m arc RS = x, from the ratios:

m arc ST = 4x

m arc TU = 4x

m arc UR = 3x

The addition of the four arcs must be equal to 360°, then:

x + 4x + 4x + 3x = 360°

12x = 360°

x = 360°/12 = 30°

(b) m arc RS = x = 30°

m arc ST = 4x = 4*30° = 120°

m arc TU = 4x = 4*30° = 120°

m arc UR = 3x = 3*30° = 90°