How do we find the equations of asymptotes and the axes intercepts? (I did the graphs via a website).
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b)
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d)
$\displaystyle y = 2^x - 4$.
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?
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 $\displaystyle y$.