Chapter 1.6, Problem 60E

Solution

The statement “The function $y=f\left(x\right)-4$ represent a translation down $4$ units of the graph of $y=f\left(x\right)$ ” is true or false..

The statement is true.

Given:

The statement “The function $y=f\left(x\right)-4$ represent a translation down $4$ units of the graph of $y=f\left(x\right)$ ”.

Concept Used:

The graph of $y=f\left(x\right)$ is translated or shifted horizontally left or right according as:

1) If $y=f\left(x-c\right)$ , then graph shifted by c units right from $y=f\left(x\right)$ .

2) If $y=f\left(x+c\right)$ , then graph shifted by c units left from $y=f\left(x\right)$ .

And, the graph of $y=f\left(x\right)$ is translated or shifted vertically up or down according as:

1) If $y=f\left(x\right)+c$ , then graph shifted by c units up from $y=f\left(x\right)$ .

2) If $y=f\left(x\right)-c$ , then graph shifted by c units down from $y=f\left(x\right)$ .

Calculation:

Consider the given statement says, “The function $y=f\left(x\right)-4$ represent a translation down $4$ units of the graph of $y=f\left(x\right)$ ”

Since, the translation $y=f\left(x\right)-c$ translates the graph of $y=f\left(x\right)$ by $c$ units down, which support the given statement. Hence, the given statement is true.

Conclusion The statement is true.