Answer:
[tex]\text{Amplitude}=6[/tex]
[tex]\text{Period}=\frac{\pi}{2}[/tex]
Domain: [tex](-\infty,\infty)[/tex]
Range: [tex][-6,6][/tex].
Step-by-step explanation:
We have been given formula of trigonometric function [tex]Y=-6\text{cos}(4x)[/tex].
We know that equation of a cosine function is [tex]Y=A\text{cos}(Bx-c)[/tex], where,
[tex]A=\text{Amplitude}[/tex],
[tex]\text{Period}=\frac{2\pi}{B}[/tex]
[tex]\text{Phase shift}=\frac{C}{B}[/tex]
Upon looking at our given function we can see that amplitude of our given function is 6.
[tex]\text{Period}=\frac{2\pi}{4}[/tex]
[tex]\text{Period}=\frac{\pi}{2}[/tex]
Therefore, the period of our given function is [tex]\frac{\pi}{2}[/tex].
Since the basic cosine function is defined for all x values and it has no domain constraints, therefore, the domain of our given function will be [tex](-\infty,\infty)[/tex].
We know that the range of basic cosine function is [tex]-1[/tex] to 1 or [tex]-1\leq \text{cos}(4x)\leq 1[/tex].
Upon multiplying the edges of range by [tex]-6[/tex] we will get,
[tex]-6\leq \text{cos}(4x)\leq 6[/tex]
Therefore, the range of our given function is [tex][-6,6][/tex].
