# How do you find the intercepts, asymptotes and graph f(x)=5^x-2?

##### 1 Answer
Dec 6, 2015

This function is simply ${5}^{x}$ shifted downwards of $2$ units. So, the only asymptote is $y = - 2$ (since the original one was $y = 0$) as $x \setminus \to - \setminus \infty$.

As for the intercepts: the $y$ intercept is found by setting $x = 0$, and you have ${5}^{0} - 2 = 1 - 2 = - 1$.
The $x$ intercept is found by setting $f \left(x\right) = y = 0$, and you have

${5}^{x} - 2 = 0 \setminus \iff {5}^{x} = 2 \setminus \iff x = {\log}_{5} \left(2\right)$.

As I already said, the graph of this function is simply the graph of ${5}^{x}$ shifted downwards of $2$ units.