SOLUTION: f(x) = (x+6/x-7) Is point (5,-12) on the graph of f? if x=1, what is f(x)? what point is on the graph of f? if f(x)=2, what is x? what points are on the graph of f? what is t

Algebra ->  Functions -> SOLUTION: f(x) = (x+6/x-7) Is point (5,-12) on the graph of f? if x=1, what is f(x)? what point is on the graph of f? if f(x)=2, what is x? what points are on the graph of f? what is t      Log On


   

Question 697267: f(x) = (x+6/x-7)
Is point (5,-12) on the graph of f?
if x=1, what is f(x)? what point is on the graph of f?
if f(x)=2, what is x? what points are on the graph of f?
what is the domain of f?
list x intercepts if any.
list y intercepts if any.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29+=+%28x%2B6%29%2F%28x-7%29
Is point (x,y)=(5,-12) on the graph of f%28x%29 or y
f%28x%29+=+%28x%2B6%29%2F%28x-7%29...plug in values for x and y
-12+=+%285%2B6%29%2F%285-7%29
-12+=+11%2F-2
-12+%3C%3E+-5.5....so, the point is not on a graph

if x=1, what is f%28x%29? what point is on the graph of f?
f%281%29+=+%281%2B6%29%2F%281-7%29

f%281%29+=+7%2F-6
f%281%29+=+-1.1666666666666666666666666666667
f%281%29+=+-1.17

point is (1,-1.17)

if f(x)=2, what is x? what points are on the graph of f?
2+=+%28x%2B6%29%2F%28x-7%29

2%28x-7%29=+%28x%2B6%29
2x-14=+x%2B6
2x-x=+14%2B6
x=+20
point is (20,2)
what is the domain of f?
since denominator is %28x-7%29 it will be equal to zero if x=7; so, the domain is all real numbers x except x=7

x-intercepts: set f%28x%29=0
0+=+%28x%2B6%29%2F%28x-7%29
0%28x-7%29+=+x%2B6
0+=+x%2B6
-6=+x......there is one x-intercept at (-6,0)
y-intercepts: set x=0
f%280%29=+%280%2B6%29%2F%280-7%29
f%280%29=+6%2F-7
f%280%29=+-0.86....there is one y-intercept at (0,-0.86)