Chapter 3.7, Problem 24E

To determine

To write: an equation that represents the transformation: horizontal translation 10 units left of the graph of $g\left(x\right)=\left|x\right|$ .

Answer to Problem 24E

  $f\left(x\right)=\left|x+10\right|$

Explanation of Solution

Concept used:

Horizontal translation:

The graph of $g\left(x\right)=f\left(x-h\right)$ is a horizontal translation of the graph of f .

The horizontal shift is h units’ right if $h>0$ and h units left if $h<0$ .

The required function is the horizontal translation 10 units left of the graph of $g\left(x\right)=\left|x\right|$ .

Since, it is the horizontal translation then by the above definition, the function is of the form $f\left(x\right)=g\left(x-h\right)$ .

Also, it is known that translation is 10 units left, it gives that $h=-10$ .

Thus, the required equation is:

  $\begin{array}{c}f\left(x\right)=g\left(x-h\right)\\ =\left|x-\left(-10\right)\right|\\ =\left|x+10\right|\end{array}$