Chapter 4, Problem 17PFR

To determine

Identify the parent function and describe the transformation shown in the graph

Answer to Problem 17PFR

  $Equationforthegraphedfunction=\left[x\right]+1$

Explanation of Solution

Given information: graph

  

Concept Used:Let $c$ be a positive real number. Vertical and horizontal shifts in the graph of $y=f(x)$ are represented as follows

1. Vertical shift ‘ $c$ ’ units upward

  $h(x)=f(x)+c$

2. Vertical shift ‘ $c$ ’ units downward

  $h(x)=f(x)-c$

3. Horizontal shift ‘ $c$ ’ units to the right

  $h(x)=f(x-c)$

4. Horizontal shift ‘ $c$ ’ units to the left

  $h(x)=f(x+c)$

Reflection in the co-ordinate axes of the graph of $y=f(x)$ are represented as follows

1. Reflection in the $x-axis$

  $h(x)=-f(x)$

2. Reflection in the $y-axis$

  $h(x)=f(-x)$

Calculation:

  $theparentfunction=\left[x\right]$

The parent function is shift of $1$ unit upward

  $Equationforthegraphedfunction=\left[x\right]+1$