Question

1. fill in the missing coordinate in each ordered pair so that the pair is a solution of $y = -3^x$. 11a \\(\left(4, -81\

ight)\\) 11b \\(\left(\square, -\frac{1}{9}\
ight)\\)

Explanation:

Step1: Substitute y into the equation

We know the equation is \( y = -3^x \), and we are given \( y = -\frac{1}{9} \). So we substitute \( y \) into the equation:
\( -\frac{1}{9} = -3^x \)

Step2: Simplify the equation

Divide both sides of the equation by -1:
\( \frac{1}{9} = 3^x \)

Step3: Express 1/9 as a power of 3

We know that \( \frac{1}{9} = 3^{-2} \) because \( 3^2 = 9 \), so \( 3^{-2}=\frac{1}{3^2}=\frac{1}{9} \). So now our equation is:
\( 3^{-2} = 3^x \)

Step4: Solve for x

Since the bases are the same (both are 3), we can set the exponents equal to each other:
\( x = -2 \)

Answer:

-2