SOLUTION: Graph the function: f(x)=(5x-1)/(-x+2) and find: a) domain and range b) equation of its asymptote c) graph its inverse d) domain and range of its inverse

Algebra ->  Graphs -> SOLUTION: Graph the function: f(x)=(5x-1)/(-x+2) and find: a) domain and range b) equation of its asymptote c) graph its inverse d) domain and range of its inverse      Log On


   



Question 1043505: Graph the function:
f(x)=(5x-1)/(-x+2)
and find:
a) domain and range
b) equation of its asymptote
c) graph its inverse
d) domain and range of its inverse

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Asymptote (vertical) at x=2.
Domain is the union of x%3C2 and x%3E2.
Root at x=1%2F5 crossing the x-axis.
Horizontal asymptote of y=-5.
You can check on range, looking near the critical x values of 1/5 and 2.

Graph the inverse?
Try setting to %285y-1%29%2F%28-y%2B2%29=x and see what you find. Is this actually a function, or not?
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5y-1=x%282-y%29
5y-1=2x-xy
5y%2Bxy-1=2x
5y%2Bxy=2x%2B1
y%285%2Bx%29=2x%2B1
highlight_green%28y=%282x%2B1%29%2F%28x%2B5%29%29
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graph%28400%2C400%2C-11%2C6%2C-9%2C8%2C%282x%2B1%29%2F%28x%2B5%29%29