Question

Give an example of an exponential function that goes through the point (-3,1)

Answer 1

`\bf \left.\qquad \qquad \right.\textit{negative exponents}\\\\ a^{-{ n}} \implies \cfrac{1}{a^( n)} \qquad \qquad \cfrac{1}{a^( n)}\implies a^{-{ n}} \qquad \qquad a^{{{ n}}}\implies \cfrac{1}{a^{-{{ n}}}}\\\\ -------------------------------\\\\`


`\bf y=a^x\quad \begin{cases} x=-3\\ y=1 \end{cases}\quad 1=a^(-3)\implies 1=\cfrac{1}{a^3}\implies a^3=\cfrac{1}{1} \\\\\\ a=\sqrt[3]{\cfrac{1}{1}}\implies a=1\qquad thus\qquad \boxed{y=(1)^x}`