Question

how is the graph of f(x)= x^2-4x be used to obatin the graph of y=g(x)?

I am stuck and unsure how to get out of this one so can you please help? thanks!


You must define g(x). Is g(x) the inverse function of f(x)?


well the function f(x)= x^2-4x has two zeros x= o and x-4


Yes. True. So what do you mean by g(x). THere has to be some specified relationship between f(x) and g(x).


okay sorry bobpursley there is a more to this questions
so it says :
draw the graphs of f(x) =x^2-4x and
g(x)= 1/ f(x) on the same grid.

I alread did that but does this tie in with the question I am so confused about?


This is the original queston;
how is the graph of f(x)= x^2-4x be used to obatin the graph of y=g(x)?
Using the relation
(1) g(x)= 1/ f(x)
we see that g(x) is the reciprocal of f(x). This should not be confused with the inverse of f(x).
The zeroes or roots of f(x) are 0 and 4. g(x) has vertical asymptotes at those points.
Yes, it does tie in with the original question. If you graph them over each other you'll see that each value of g(x) satisfies the relation (1) you gave above.