# Thread: Need the asymptotes and the axes intercepts Of these graphs

1. ## Need the asymptotes and the axes intercepts Of these graphs

How do we find the equations of asymptotes and the axes intercepts? (I did the graphs via a website).

a)

b)

c)

d)

2. $\displaystyle y = 2^x - 4$.

It's important to note for exponential functions such as $\displaystyle y = a^x$ that $\displaystyle y > 0$ for all $\displaystyle x$.

So for $\displaystyle y = 2^x - 4$, if you know $\displaystyle 2^x > 0$, then what do you think $\displaystyle 2^x - 4$ is greater than?

3. Originally Posted by Prove It
[tex] then what do you think $\displaystyle 2^x - 4$ is greater than?
y= - 4

4. Correct. So $\displaystyle y = -4$ is an asymptote.

Now going back to the original equation

$\displaystyle y = 2^x - 4$.

To find the $\displaystyle x$ intercept, let $\displaystyle y = 0$ and solve for $\displaystyle x$.

To find the $\displaystyle y$ intercept, let $\displaystyle x = 0$ and solve for $\displaystyle y$.