Chapter 2.5, Problem 62AYU

To determine

To sketch: graph of the given function using technique of transformation. Also find the domain and range.

Answer to Problem 62AYU

Domain is all real numbers and range is all integers.

Explanation of Solution

Given information:

Given function

  $h\left(x\right)=\mathrm{int}\left(-x\right)$

Calculation:

Let us consider the graph of the function $f\left(x\right)=x$

  

Now $f\left(x\right)=x$ , whose domain and range is all real numbers.

Now, reflect the graph about $x$ axis or $y$ axis, the function becomes

  $f_1\left(x\right)=-x$ , whose domain and range is all real numbers.

Now, apply the absolute on the function, the function; then, transforms into

  $h\left(x\right)=\mathrm{int}\left(-x\right)$ , whose domain is all real numbers and range is all integers.

Its graph is as follows