what are the x - intercepts of the graph of the function $y = 6\tan(\frac{x}{2})-3$? use your graphing…

Explanation:

Step1: Set y = 0

Set $6\tan(\frac{x}{2})-3 = 0$.

Step2: Solve for $\tan(\frac{x}{2})$

Add 3 to both sides: $6\tan(\frac{x}{2})=3$. Then divide by 6: $\tan(\frac{x}{2})=\frac{3}{6}=\frac{1}{2}$.

Step3: Find the principal - value of $\frac{x}{2}$

Using the inverse - tangent function, $\frac{x}{2}=\arctan(\frac{1}{2})\approx0.4636$.

Step4: Find the general solution for $\frac{x}{2}$

The general solution for $\tan\theta = k$ is $\theta=\arctan(k)+n\pi$, where $n$ is an integer. So, $\frac{x}{2}=0.4636 + n\pi$.

Step5: Solve for x

Multiply both sides by 2: $x = 0.9273+2n\pi$, where $n$ is an integer.

Answer:

C. $(0.9273 + 2n\pi,0)$, where $n$ is any integer