What is the asympote of this graph?

[priscilla98]

Homework Statement

How come the graph of y = 2^x has a negative x-axis as an asympote. And what is the asympote of this graph?

Homework Equations

An asympote is a line that approaches the graph but does not intersect as x increases or decreases.

The Attempt at a Solution

I know the graph of y = 1/2^x has an asympote which is y = 0 because its closer to the y=0. But for y= 2^x, i only see the numbers increasing, would the asympote be y = - 2

 

[Mark44]

Homework Statement

How come the graph of y = 2^x has a negative x-axis as an asympote. And what is the asympote of this graph?

Because as x gets more and more negative, y = 2^x gets closer to zero. The horizontal asymptote is the line y = 0.

Homework Equations

An asympote is a line that approaches the graph but does not intersect as x increases or decreases.

I think you have this backwards. An asymptote is a line that the graph approaches. A curve can intersect or cross a horizontal asymptote for values of |x| that are relatively small, but won't intersect or cross when x is large or is very negative.

The Attempt at a Solution

I know the graph of y = 1/2^x has an asympote which is y = 0 because its closer to the y=0. But for y= 2^x, i only see the numbers increasing, would the asympote be y = - 2

y = 2^x is defined for all real numbers x. You're focusing on large values of x. The curve is asymptotic to the x-axis for x approaching -infinity. The graphs of y = 2^x and y = 2^(-x) are reflections of each other across the y-axis, so if one has the positive x-axis as its horizontal asymptote (y = 2^(-x) = 1/2^x), the other will have the negative x-axis as its horizontal asymptote.

 

[Willian93]

in the graph 2^x, doesn't matter what value for x, y NEVER can be zero or negative, because this is exponential relation. try x=-100000000, y is extremely small but can never be zero. The asymptote for that graph is y=0, where y can never approach value closer to zero.