the function g is given by g(x) = 2 tan(x - 3) + 5. which of the following could be coordinates for an…

Explanation:

Step1: Recall inflection - point property of tangent function

The tangent function (y = A\tan(Bx - C)+D) has inflection - points where the second - derivative changes sign. For the basic tangent function (y = \tan x), the inflection - points occur at (x = \frac{k\pi}{2}), (k\in\mathbb{Z}). For the function (g(x)=2\tan(x - 3)+5), we set (x-3=\frac{k\pi}{2}), (k\in\mathbb{Z}).

Step2: Solve for (x)

[x=\frac{k\pi}{2}+3]

Step3: Find (x) in the domain ((0,10))

When (k = 0), (x = 3).

Step4: Find the (y) - value

Substitute (x = 3) into (g(x)): (g(3)=2\tan(3 - 3)+5=2\tan(0)+5=5)

Answer:

C. ((3,5))