SOLUTION: Sketch the graph of f(x) = x^2 - 2x and use the graph to sketch the reciprocal function. Explain how you were able to do this from the graph of f(x).

Algebra ->  Functions -> SOLUTION: Sketch the graph of f(x) = x^2 - 2x and use the graph to sketch the reciprocal function. Explain how you were able to do this from the graph of f(x).       Log On


   

Question 1204828: Sketch the graph of f(x) = x^2 - 2x and use the graph to sketch the reciprocal function. Explain how you were able to do this from the graph of f(x).
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29+=+x%5E2+-+2x+
f%28x%29+=+%28x%5E2+-+2x+%2Bb%5E2%29-b%5E2
f%28x%29+=+%28x%5E2+-+2x+%2B1%5E2%29-1%5E2
f%28x%29+=+%28x+-+1%29%5E2-1 => it’s parabola with vertex at (1,-1)
axes of symmetry is x=1
the domain of f%28x%29 is all real numbers
To find the x-intercepts, we can set f%28x%29=+0
x%5E2+-+2x+=0
x%28x+-+2%29+=0
the x-intercepts are
x=0
x=2
make table
x|y
0|0
2|0
1|-1
-1|3
3|3
-2|8
plot points and draw a graph




The reciprocal of this would be
f%28x%29++=+1%2F%28+a%28x+-+h%29%5E2+%2B+k%29
This is a rational function.
f%28x%29+=+1%2F%28%28x+-+1%29%5E2-1++%29
vertical asymptote will be at x=0 and x=2 (x-intercepts of given function)
make table

x|y
0|0
2|0
1|-1
-1|1%2F3
3|1%2F3
-2|1%2F8
plot the points and graph