Question

Please #21 A ) state the domain B) state the rangeC) graph the relation D) is it a function E) is it a one to one

Answer 1

To answer the question, let us make a graph of the equation

`\mleft\lbrace(x,y\mright)\colon|x|+|y|\leq2\text{ and }|y|\leq1\}`

The graph is shown below

(A) From the graph, the domain is determined from the x-axis. The domain is from -2 to +2,

Hence, the domain is

`\lbrack-2,2\rbrack`

(B) The range is determined from the y-axis. The range from the graph is -1 to 1

Hence the range is

`\lbrack-1,1\rbrack`

(C) We have the graph above already

(D) It is not a function because some values on the x-axis has two values on the y-axis. for example, where

`\begin{gathered} x=-1 \\ y=-1\text{ and 1} \end{gathered}`

A function should have only one y value for each values of x.

Hence, it is not a function

(E) Since it is not a function, it is therefore not a one-to-one function

Hence, it is not a one-to-one function.