Answer:
y = tan(1/2 x + π/2) ⇒ answer c
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)