a function h is defined as h(x)=7 tan(2(x - 4)+5). which of the following statements is true? the values 2…

Explanation:

Step1: Recall tangent - function domain and asymptotes

The general form of the tangent function is $y = A\tan(B(x - C))+D$. The domain of $y = \tan(x)$ is all real numbers except $x=\frac{\pi}{2}+k\pi,k\in\mathbb{Z}$. For the function $y = A\tan(B(x - C))+D$, the vertical asymptotes occur at $B(x - C)=\frac{\pi}{2}+k\pi,k\in\mathbb{Z}$, and the domain is all real numbers except the solutions of $B(x - C)=\frac{\pi}{2}+k\pi$.

Step2: Identify parameters in the given function

Given $h(x)=7\tan(2(x - 4)) + 5$, where $A = 7$, $B = 2$, $C = 4$, and $D = 5$.

Step3: Find the vertical - asymptotes equation

Set $2(x - 4)=\frac{\pi}{2}+k\pi,k\in\mathbb{Z}$. Solving for $x$ gives $x=4+\frac{\pi}{4}+\frac{k\pi}{2},k\in\mathbb{Z}$. The values of $B = 2$ and $C = 4$ are used to find the location of the vertical asymptotes and also affect the domain (since the domain excludes the values of $x$ that make the argument of the tangent function equal to $\frac{\pi}{2}+k\pi$). The values $A = 7$ and $D = 5$ affect the range and the vertical - shift of the function, but not the domain or the location of the vertical asymptotes.

Answer:

The values 2 and 4 affect the domain and the location of the vertical asymptotes of the function $h(x)$.