why cant y = 2^x have a x intercept?

Question

college algebra - solve

Answer 1

Check out some values.

x, y
0, 1
-1, 1/2
-2, 1/4
...

1, 2
2, 4
3, 8
...

There are no values of x that yield y = 0!

Answer 2

Look at the graph of y = 2^x
It has an asymptote at the x axis, which means that it will get closer and closer, but never touch.
Try some numbers:
y = 2 ^ 2 = 4
y = 2^ 0 = 1
y = 2 ^ -9999 = 1 / (2^9999)
2 ^ 9999 is a very large number, and 1 / that is a really small number. So as the number gets smaller and smaller(negative), a calculator will give you 0; because it is so close to 0, it cannot give a number any smaller. In reality, the number is extremely small, but not actually zero.

Answer 3

At x intercept y = 0.
and log 1 = 0.

y = 2^x
log y = log 2^x
log 1 = x log 2
log 1/ log 2 = x
0 / 0∙301 029 995 ... = x
x = ??????????

When x has a very small value, if it does not intercept with the y axis, it gets very close to it.

2^ -100,000 = 0
2^ -200,000 = 0 etc.

Answer 4

y=2^x can't be an x-intercept because it is an exponential function meaning it has a horizontal asymptote at y=0 - so the function gets very close to 0 but can't reach it [x-intercept means where the function crosses the x-axis].

Answer 5

This means for some value of x, y=0.
Is this possible?
Well, that means 0=2^x, or take the log of both sides, log0=xlog2.
But, there doesn't exist a real value of log0!
Therefore, it can't have a x intercept!

Answer 6

It cannot because there is no power to which any number can be raised which results in 0. Therefore, since a^x can never equal zero, y cannot ever equal zero and therefore, since y can never equal zero in this equation, there is no x-intercept.

Answer 7

2^x = 0 has no solution. 2^x is always > 0.

Answer 8

Because y can never be negative, thus it will not be able to cross the x axis

Answer 9

There are no x-intercepts, here are some examples:
(0,1) (1,2) (2,4) (3,8) (4,16)

Answer 10

because it is asymptotic to x axis