1. **State the problem:** Find the equation of the exponential function passing through points $(-1,1)$ and $(0,3)$. 2. **Recall the general form:** An exponential function can be written as $y = ab^x$, where $a$ is the initial value and $b$ is the base. 3. **Use the point $(0,3)$:** Substitute $x=0$ and $y=3$ into $y=ab^x$ to find $a$. $$3 = a b^0 = a \times 1 = a$$ So, $a = 3$. 4. **Use the point $(-1,1)$:** Substitute $x=-1$ and $y=1$ into $y=3b^x$. $$1 = 3 b^{-1} = 3 \times \frac{1}{b} = \frac{3}{b}$$ 5. **Solve for $b$:** Multiply both sides by $b$ and divide both sides by 1 to isolate $b$. $$1 = \frac{3}{b} \implies b = 3$$ 6. **Write the final equation:** Substitute $a=3$ and $b=3$ into the general form. $$y = 3(3)^x$$ **Answer:** The correct equation is $y = 3(3)^x$.