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!

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- Nov 29th 2012, 03:53 AMTutuWhat 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! - Nov 29th 2012, 05:06 AMearbothRe: What does it mean?
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)

2. With your equation

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

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. ( $\displaystyle \lim_{x \to -\infty}(f(x)) = 0$)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. - Nov 29th 2012, 06:46 AMTutuRe: 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 - Nov 29th 2012, 07:23 AMHallsofIvyRe: 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?