$($a$)$ Write an equation that deflnes the exponential function with base a $>0.$

$f(x)=a^x$

$f(x)=e^{\frac{a}{x}}$

$f(x)=x^2$

$f(x)=lo{g}_{2}x$

$f(x)=a{e}^x$

$($b$)$ What is the domain of this function? $($Enter your answer using interval notation.$)$

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$($c$)$ If a $4,$ what is the range of this function? $($Enter your answer using interval notation$)$

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