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.
To obtain the graph of y=g(x) from the graph of f(x)= x^2-4x, you need to apply the relationship g(x)= 1/ f(x).
Here's how you can proceed:
1. Start by graphing f(x)= x^2-4x. This is a quadratic function and can be sketched by finding the x-intercepts (zeros) and vertex of the parabola.
2. The zeros or roots of f(x) are x=0 and x=4. Mark these points on the x-axis of your graph.
3. Next, plot a few additional points on the graph of f(x) by substituting different x-values into the equation f(x)= x^2-4x and finding the corresponding y-values.
4. Now, evaluate g(x) by substituting each y-value of f(x) into the expression g(x)= 1/ f(x). This will give you the corresponding values of g(x).
5. Plot these points on a separate graph, using the same x-values as in the graph of f(x), but with the corresponding y-values of g(x).
6. Connect the points on the graph of g(x) with a smooth curve. Note that g(x) has vertical asymptotes at the points where f(x) has zeros.
7. Finally, compare the graph of f(x) with the graph of g(x). You will see that each value of f(x) corresponds to a value of g(x) that satisfies the relationship g(x)= 1/ f(x).
By following these steps, you can obtain the graph of y=g(x) from the graph of f(x)= x^2-4x.