\( y=2(9)^{x} \) for \( x=-2,0 \), and \( \frac{1}{2} \)

Sure! Let's evaluate the function \( y = 2 \times 9^{x} \) for the given values of \( x \): \[ y = 2 \times 9^{x} \] ### 1. When \( x = -2 \): \[ \begin{align*} y &= 2 \times 9^{-2} \\ &= 2 \times \left(\frac{1}{9}\right)^{2} \\ &= 2 \times \frac{1}{81} \\ &= \frac{2}{81} \\ &\approx 0.0247 \end{align*} \] ### 2. When \( x = 0 \): \[ \begin{align*} y &= 2 \times 9^{0} \\ &= 2 \times 1 \quad \text{(since any number raised to the power of 0 is 1)} \\ &= 2 \end{align*} \] ### 3. When \( x = \frac{1}{2} \): \[ \begin{align*} y &= 2 \times 9^{\frac{1}{2}} \\ &= 2 \times \sqrt{9} \\ &= 2 \times 3 \\ &= 6 \end{align*} \] ### Summary of Results: | \( x \) | \( y = 2 \times 9^{x} \) | Approximate Value | |---------------|---------------------------|--------------------| | \( -2 \) | \( \frac{2}{81} \) | \( \approx 0.0247 \) | | \( 0 \) | \( 2 \) | \( 2 \) | | \( \frac{1}{2} \) | \( 6 \) | \( 6 \) | If you need any further assistance or additional evaluations, feel free to ask!