Is it true or false that the function ';f(x)=3x'; grows three times faster than the function';g(x)=x.'; Explain .

true becuz in the first funtion, x is multipliedby 3 each time i thinkIs it true or false that the function ';f(x)=3x'; grows three times faster than the function';g(x)=x.'; Explain .
True because f(x) = 3x = 3 * g(x)





Or





Think of a ratio of f(x)/g(x) = (3x)/x = 3 iff x is not 0





Or





Think of a change in inputs. If I add an amount n to the input of


f(x), I should get an increase 3 times that n added to the output.





f(x + n) = 3(x+n) = 3x + 3n = f(x) + 3n.





But when I add the same n to g(x), I only get g(x+n) = x+n =


g(x) + n.





So an increase of n to the input creates an increase of 3n to the output of f(x) but only n to g(x). f(x) is increasing 3 times as fast as g(x).