Chapter 3.6, Problem 51E

To determine

To find: the graph which are related by its translation and explained.

Answer to Problem 51E

Graph $F$ is vertical translation $2$ unit down of graph $A$ and Graph $C$ is a vertical translation $4$ unit up of the graph $B$ .

Explanation of Solution

Given:

  

Concept used:

In a geometry vertical translation is a translation of a geometric object in a direction parallel to the vertical axis of the cartesian coordinate system.

  $y=f\left(x\right)+k$ is the vertical translation of the graph $y=f\left(x\right)$ .

Calculation:

Here, by checking the given graph it can be easily estimate the vertical translation as:

Graph $F$ is vertical translation $2$ unit down of graph $A$ .

If graph $A$ is given by the function $f\left(x\right)$ then the graph $F$ is $f\left(x\right)-2$ .

Graph $C$ is a vertical translation $4$ unit up of the graph $B$ .

If graph $B$ is given by the function $f\left(x\right)$ then the graph $C$ is $f\left(x\right)+4$ .

Hence, Graph $F$ is vertical translation $2$ unit down of graph $A$ and Graph $C$ is a vertical translation $4$ unit up of the graph $B$ .