Question

Choose the function whose graph is given by:

Answer 1

y = tan (x-pi)-1

Explanation:

The function in the graph is a periodic function with intervals of pi and having discontinuities at regular intervals.

Hence this must be a transformation of the original trignometric funciton

tan x. y intercept is at -1 which shows that there is a vertical shift of 1 unit down.

Hence the funciton is y = tanx-1

But tan x is not given in any of the options.

Let us check which is equivalent to tan x-1

We find that tan(x-pi) = -tan (pi-x) = -(-tanx) = tanx

Hence the option 3 is the right answer

Answer 2

y = tan(x -π) -1

Explanation:

It looks like a straight tangent function shifted down one unit. Since the tangent function has a period of π, ...

tan(x -π) = tan(x)

so you're only looking for the function that has a translation downward of 1 unit. Of course that translation is accomplished by adding -1 to the original function.

The appearance of the graph is of ...

y = tan(x) -1

The choice that is equivalent to this is ...

y = tan(x -π) -1