Question

Which function is represented in this graph

Answer 1

Answer:

y = tan(1/2 x + π/2) ⇒ answer c

Step-by-step explanation:

* Lets revise some fact of y = tanx

- The domain of tanx is all x(≠ π/2) + nπ, where n is the number of cycle

- The range is all real numbers

- The period of tanx is π ÷ coefficient of x

* Lets revise some transformation

- A horizontal stretching is the stretching of the graph away from

 the y-axis

• if 0 < k < 1 (a fraction), the graph is f (x) horizontally stretched by

 dividing each of its x-coordinates by k (x × 1/k)

- A horizontal compression is the squeezing of the graph toward

 the y-axis.

• if k > 1, the graph f (x) horizontally compressed by dividing each

 of its x-coordinates by k. (x × 1/k)

* Look to the graph of y = tanx ⇒ red graph

- the graph of tanx intersect x-axis at the origin

- The period of tanx is π

* Look to the blue graph (the problem graph)

∵ The graph intersect x-axis at points (-π , 0)

- That means the graph of tanx moved to the left by π units

∴ y = tan(x + π)

- The period of the graph is 2π

∵ The period = π/coefficient of x

∴ 2π = π/coefficient of x ⇒ using cross multiplication

∴ Coefficient of x = π/2π = 1/2

- That means the graph stretched horizontally

∴ y = tan1/2(x + π)

* y = tan(1/2 x + π/2)