Question 64940: Please help! Sketch a graph of the function f(x) = 2 - log2(x - 2). Label at least three points, and show any asymptotes as dotted lines. Answer by venugopalramana(3286) (Show Source):
You can put this solution on YOUR website! Please help! Sketch a graph of the function f(x) = 2 - log2(x - 2). Label at least three points, and show any asymptotes as dotted lines.
Y = 2- LOG(X-2)/LOG(2).........SINCE LOG(N) TO BASE 'B' = LOG(N)/LOG(B) TO ANY COMMON BASE
SINCE LOG OF 0 OR NEGATIVE NUMBER DO NOT EXIST, X>2
AS X TENDS TO 2, Y TENDS TO INFINITY SINCE LOG(0) IS -INFINITY
HENCE X=2 IS A VERTICAL ASYMPTOTE.
THERE ARE NO OTHER ASYMPTOTES.
PLOT THE GRAPH USING THE FOLLOWING POINTS AND THE ASYMPTOTE GIVEN AND THE FACT THAT AS X TENDS TO INFINITY, Y ALSO TENDS TO INFINITY
X = ..........4..........6 ..........10.....18........34........ETC
Y = ..........1..........0............3.....4.........5.........ETC
