Question

Find the domain, period, range and amplitude of the cosine function. Y=-6cos4x

Answer 1

Amplitude=6
Period=pi/2
Domain=all real numbers
Range=from -6 to 6

Answer 2

Answer:

$\text{Amplitude}=6$

$\text{Period}=\frac{\pi}{2}$

Domain: $(-\infty,\infty)$

Range: $[-6,6]$.

Step-by-step explanation:

We have been given formula of trigonometric function $Y=-6\text{cos}(4x)$.

We know that equation of a cosine function is  $Y=A\text{cos}(Bx-c)$, where,

$A=\text{Amplitude}$,

$\text{Period}=\frac{2\pi}{B}$

$\text{Phase shift}=\frac{C}{B}$  

Upon looking at our given function we can see that amplitude of our given function is 6.

$\text{Period}=\frac{2\pi}{4}$

$\text{Period}=\frac{\pi}{2}$

Therefore, the period of our given function is $\frac{\pi}{2}$.

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 $(-\infty,\infty)$.

We know that the range of basic cosine function is $-1$ to 1 or $-1\leq \text{cos}(4x)\leq 1$.

Upon multiplying the edges of range by $-6$ we will get,

$-6\leq \text{cos}(4x)\leq 6$

Therefore, the range of our given function is $[-6,6]$.