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

`\text{Amplitude}=6`

`\text{Period}=(\pi)/(2)`

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

Range:
`[-6,6]`.

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}=(2\pi)/(B)`

`\text{Phase shift}=(C)/(B)`

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

`\text{Period}=(2\pi)/(4)`

`\text{Period}=(\pi)/(2)`

Therefore, the period of our given function is
`(\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]`.