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.

## Answer This Question

## Related Questions

- graphing exponential function - P(x) = -(x-a)^4 (x-b)^3 (x-c) where a>0, b<...
- College Algebra - 1.The graph of y = - 1/2 |x - 5| - 3 can be obtained from the ...
- Algebra help! - I dont understand my problems that I am suppose to do. please ...
- calculus - #3 A solid has a base in the form of the ellipse: x^2/25 + y^2/16 = 1...
- calculus - 1.Find the following for the function f(x)=(x+6)^2(x-2)^2 a. what are...
- Calculus-Derivatives - You have been asked to determine whether the function f(x...
- Math - f(x) is a linear function which is increasing for XER. a) Will the ...
- algebra - Which of the following best describe the graph of a quadratic equation...
- science/maps - Could contour lines on a map ever cross? Explain please
- algebra - HELP!!!!!!!!!!!!! write equation of a polynomial function with the ...

More Related Questions