Question

Graph the following function then provide the domain and range using set notation. Show at least 4 "steps". I have plotted the graph correctly, I used random numbers as x to solve for why then plotted those points....I know the Domain is -infinity to infinity and same with the range....but I dont know how to put -infinity to infinity into set notation. Please help and thank you.

Answer 1

Given:

The given function is,

$y=\lbrack\frac{1}{2}x\rbrack+1$

The objective is to plot the graph and find the domain and range in set notation.

Explanation:

FIrst, the graph fo the function will be,

To find domain:

Domain represents the interval of the graph from negative x-axis to positive x-axis.

It can be observed from the graph that domain of the function lies in the interval of all real numbers as,

$D(-\infty,+\infty),\mleft\lbrace x│x\epsilon\R\mright\rbrace$

To find range:

Range represents the interval of the graph from negative y-axis to positive y-axis.

It can be observed from the graph that the range o the function lies in the interval of all real numbers as,

$R(-\infty,+\infty),\lbrace y│y\epsilon\R\rbrace$

Hence,

The domain of the function is D {x│x∈ℝ}.

The range of te function is R {y│y∈ℝ}.