Answer to Question #291833 in Real Analysis for Nikhil

Question

Sketch the graph of the function, f defined by

f(x)= |x-3| +[x], x∈ [2,4] where [x] denotes the greatest integer function

Answer 1

Solution:

$f(x)=y\:=|x-3|\:+\left[x\right], x∈ [2,4]$

$\mathrm{Domain\:of\:}\:y\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:2\le \:x\le \:4\:\\ \:\mathrm{Interval\:Notation:}&\:\left[2,\:4\right]\end{bmatrix}$

$\mathrm{Range\:of\:}y:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:3\le \:f\left(x\right)\le \:5\:\\ \:\mathrm{Interval\:Notation:}&\:\left[3,\:5\right]\end{bmatrix}$

$\\ \mathrm{Extreme\:Points\:of}\ y:\quad \mathrm{Maximum}\left(4,\:5\right)$

Using this data, its graph is: