Note that both the numerator and denominator approach 0 as
, so we can try using L'Hopital's rule.
The denominator is nonzero at
, so the limit is equivalent to
You see if the graphs passes the vertical line test.
if any vertical line passes through more than one part of the graph then its not a function - just a relation.
Think and do the math take your time
The veretx is normally the minimum value
hack:
for f(x)=ax²+bx+c
the x value of the vertex is -b/2a
so
f(x)=1x²-16x+71
x value is -(-16)/(2*1)=16/2=8
find f(8) to find y value of vertex
f(8)=8²-16(8)+71
f(8)=64-128+71
f(8)=7
the vertex is (8,7)
the minimum value is 7
