Match the function with its graph.

The answer is 1D , 2A , 3C , 4B ⇒ answer (c)

Step-by-step 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)

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step-by-step explanation: