Answer:
The answer is 1D , 2A , 3C , 4B ⇒ answer (c)
Explanation:
* Lets talk about the transformation
- If the function f(x) reflected across the x-axis, then the new
function g(x) = - f(x)
- If the function f(x) translated horizontally to the right
by h units, then the new function g(x) = f(x - h)
- If the function f(x) translated horizontally to the left
by h units, then the new function g(x) = f(x + h)
* Lets explain each function
∵ y = tan(x)
∵ y = -tan(x - π/2)
# (x - π/2) means the graph translated horizontally to
the right π/2 units
# -tan(x - π/2) means the graph reflected across the x-axis
∴ The graph is (D)
* 1) y = -tan(x - π/2) ⇒ (D)
∵ y = tan(x + π/2)
# (x + π/2) means the graph translated horizontally to
the left π/2 units
∴ The graph is (A)
* 2) y = -tan(x - π/2) ⇒ (A)
∵ y = -cot(x - π/2)
# (x - π/2) means the graph translated horizontally to
the right π/2 units
# -cot(x - π/2) means the graph reflected across the x-axis
∴ The graph is (C)
* 3) y = -cot(x - π/2) ⇒ (C)
∵ y = cot(x + π/2)
# (x + π/2) means the graph translated horizontally to
the left π/2 units
∴ The graph is (B)
* 4) y = -tan(x - π/2) ⇒ (B)
∴ The answer is 1D , 2A , 3C , 4B answer (c)