1. **State the problem:** We need to find the exponential function $y = ab^x$ that passes through the points $(-1, 0.75)$, $(0, 1.5)$, and $(1, 3)$. 2. **Recall the general form:** An exponential function is $y = ab^x$, where $a$ is the initial value (when $x=0$) and $b$ is the base or growth factor. 3. **Use the point $(0, 1.5)$ to find $a$:** Since $y = ab^x$, plugging in $x=0$ gives $y = a b^0 = a \cdot 1 = a$. So, $a = 1.5$. 4. **Use the point $(1, 3)$ to find $b$:** Plug in $x=1$, $y=3$: $$3 = 1.5 \times b^1 = 1.5b$$ Divide both sides by 1.5: $$\frac{3}{\cancel{1.5}} = \cancel{1.5}b \Rightarrow 2 = b$$ 5. **Verify with the point $(-1, 0.75)$:** Plug in $x=-1$, $y=0.75$: $$0.75 = 1.5 \times 2^{-1} = 1.5 \times \frac{1}{2} = 0.75$$ This confirms our values are correct. 6. **Final exponential function:** $$y = 1.5 \times 2^x$$