Posted by carl on Wednesday, August 17, 2011 at 3:16pm.
Does the function y = 2^x ever cross the xaxis? Explain why or why not

algebra  Henry, Thursday, August 18, 2011 at 12:22am
The point where the function crosses the xaxis is call the xintercept or
solution. Y equals zero at the point where the graph croses the xaxis. If
Y never goes to zero, the function does not cross or touch the xaxis.
It can be proven that the graph of the
given Eq does not cross or touch the xaxis for any real value of x:
Let x = 0,
Y = 2^x = 2^0 = 1.
So when x is positive, the minimum value of Y is 1.
Let x = 10.
Y = 2^10 = 1/2^10 = 0.0009766.
The value of y approaches zero as a
limit, but can never reach zero unless
the numerator equals zero. But the numerator = 1.
Let y = 0.
y = 2^x = 0,
Take log of both sides:
xlog2 = log(0),
X = log(0)/log2,
But the log of 0 is undefined. Therefore, there is no real value of
x that will give a y of 0.
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