# Math Help - What does it mean?

1. ## What does it mean?

Hi this is a question regarding terminology.

For the function y = (4^x) - (2^x), find the axes intercepts.

What does axes intercept mean?

Thank you!

2. ## Re: What does it mean?

Originally Posted by Tutu
Hi this is a question regarding terminology.

For the function y = (4^x) - (2^x), find the axes intercepts.

What does axes intercept mean?

Thank you!
1. If the graph of your function intercepts the x-axis then y = 0;
if the graph of your function intercepts the y-axis then x = 0.

Normally you have 2 intercepts (because you have 2 axes)

$y = 4^x-2^x = 2^x(2^x-1)$

you easily can see that the graph passes through the origin, that means the x-axis and the y-axis are intercepted simultaneously in one point.

3. Be aware that the graph of your function has the x-axis as asymptote. ( $\lim_{x \to -\infty}(f(x)) = 0$)So maybe (depending on the contents of your math lessons) the "improper" point at the left end of the x-axis is called a x-axis intercept too.

3. ## Re: What does it mean?

Thanks!

Sorry could you explain a little more in detail, why the x-axis is the asymptote?

Also, so can I say that the intercepts are at
When the curve intersects the x-axis, y=0
When the curve intersects the y-axis, x-0

4. ## Re: What does it mean?

I suggest you review your basic definitions. An "intercept" is where a graph crosses a specific line- an x-intercept is where the graph crosses the x-axis (and so where y= 0), a y-intercept is where the graph crosses the y- axis (and so where x= 0). An "asyptote" is a straight line that a graph approaches nearer and nearer as at least one of the variables goes to infinity or negative infinity. As earboth pointed out, [tex]y= e^{4x}- e^{2x}= e^{2x}(e^{2x}- 1)[/itex]. What happens as x goes to negative infinity?