The function that translates every point of the function f(x) 5 units above can be represented by g(x)=log₂x + 5.
A function assigns the value of each element of one set to the other specific element of another set.
As the function that is given to us is f(x)=log₂x, therefore, the function can be written as,
[tex]y=f(x)=\rm log_2x[/tex]
Now, since we need every point to be up by 5 units, therefore, every value of x should be +5 on the y axis, therefore, the function that will represent that every point up by 5 units of the function f(x) can be written as,
[tex]g(x) = y+ 5\\\\g(x) = f(x) + 5\\\\g(x) = {\rm log}_2x + 5[/tex]
Hence, the function that translates every point of the function f(x) 5 units above can be represented by g(x)=log₂x + 5.
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