Question

f(x)=|1/3x| translation 2 units to the left

Answer 1

$f(x)=\left|\dfrac{1}{3}x\right|\xrightarrow{T_{\vec{a}= <-2;\ 0 >}}g(x)=f(x+2)=\left|\dfrac{1}{3}(x+2)\right|=\left|\dfrac{1}{3}x+\dfrac{2}{3}\right|$

Look at the picture.

Answer 2

Answer:

$f(x)=\frac{1}{3}|(x+2)|$

Step-by-step explanation:

We have been given a function $f(x)=|\frac{1}{3}x|$. We are asked to translate the function to 2 units to the left.

We know that an absolute function is form $y=a|x-h|+k$, where, (h,k) is vertex.

Let us recall translation rules.

$f(x)\rightarrow f(x-a)=\text{Graph shifted to right by a units}$  

$f(x)\rightarrow f(x+a)=\text{Graph shifted to left by a units}$

$f(x)\rightarrow f(x)+a=\text{Graph shifted upwards by a units}$  

$f(x)\rightarrow f(x)-a=\text{Graph shifted downwards by a units}$

Absolute value of 1/3 will be 1/3.

$f(x)=\frac{1}{3}|x|$

Therefore, our required function would be $f(x)=\frac{1}{3}|x+2|$.