Question

Y=cosx Can you please give a graph use color for function, asymptotes, etc.A short table of easy pointsThe domain and rangePlease identify and label the asymptotes (Please work this as if you didn’t have a calculator)

Answer 1

We will have the following:

We are given:

$y=\cos (x)$

We will construct a table from 0 to 10, that is:

$\begin{cases}f(0)=\cos (0)\Rightarrow f(0)=1 \\ \\ f(1)=\cos (1)=0.5403023059\ldots \\ \\ f(2)=-0.4161468365\ldots \\ \\ f(3)=-0.9899924966\ldots \\ \\ f(4)=-0.6536436209\ldots \\ \\ f(5)=0.2836621855\ldots \\ \\ f(6)=0.960101702867\ldots \\ \\ f(7)=0.7539022543\ldots \\ \\ f(8)=-0.1455000338\ldots \\ \\ f(9)=-0.9111302619\ldots \\ \\ f(10)=-0.8390715291\ldots \\ \end{cases}$

From this we can see that the function is periodic in nature and fluctuates between the values of y = 1 and y = -1, this can be seing as follows:

Now, from this we can obtain the domain and range:

$\text{Dom}_f=(-\infty,\infty)$$\text{Ran}_f=(-1,1)$

There are not asymptotes, but the maximum and minimum values the function will ever reach are y = 1 & y = -1 respectively.