Question

The function f(x) = 1/5 is translated up 4 units. Which equation represents the translated function?

Answer 1

To translate a function upwards by 4 units, you add a constant of four to the function.

If f(x) truly is just a constant 1/5 which is just a horizontal line...

f(x)+4=1/5+4

g(x)=(1+20)/5

g(x)=21/5

g(x)=4.2

Answer 2

The equation that represents the translated function for

$\rm f(x) = \dfrac{1}{5}$   $\rm is\;\; \rm \bold{g(x) = f(x) +4 = 4.2}$.

Given that the function f(x) = 1/5 is translated up 4 units.  

We have to determine the equation that  represents the translated function

The function f(x) = 1/5  as the function is translated.    

Translation is a concept of mathematics . In translation the shape of the object is simply moved linearly from one point to other point by adding some constant values in the previous coordinates. In translation , there  is no dilation shape and size of the object remains the same.

Let us consider that if the function is translated up with 4 units then the new function is $\rm\bold{ g(x)}$

So according to the language of question we

$\rm g(x) = f(x) +4$

$\rm g(x) = \dfrac{1}{5} +4 = \dfrac{21}{5} = 4.5$

$\rm g(x) = 4.5$

The equation that represents the translated function for

$\rm f(x) = \dfrac{1}{5}$      $\rm is\;\; g(x) = f(x) +4 = 4.2$

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