Posted by **carl** on Wednesday, August 17, 2011 at 3:16pm.

Does the function y = 2^x ever cross the x-axis? Explain why or why not

- algebra -
**Henry**, Thursday, August 18, 2011 at 12:22am
The point where the function crosses the x-axis is call the x-intercept or

solution. Y equals zero at the point where the graph croses the x-axis. If

Y never goes to zero, the function does not cross or touch the x-axis.

It can be proven that the graph of the

given Eq does not cross or touch the x-axis 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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