graphing exponential functions\nexploring exponential functions: $y = b^x, 0 < b < 1$\ncomplete the table of…

graphing exponential functions\nexploring exponential functions: $y = b^x, 0 < b < 1$\ncomplete the table of values for the function\n$f(x) = \\left(\\frac{1}{3}\\right)^x$\n\n| $x$ | $-2$ | $-1$ | $0$ | $1$ | $2$ || ---- | ---- | ---- | ---- | ---- | ---- || $f(x)$ | $a$ | $b$ | $c$ | $\\frac{1}{3}$ | $\\frac{1}{9}$ |$a=\\square$\n$b=\\square$\n$c=\\square$

graphing exponential functions\nexploring exponential functions: $y = b^x, 0 < b < 1$\ncomplete the table of values for the function\n$f(x) = \\left(\\frac{1}{3}\\right)^x$\n\n| $x$ | $-2$ | $-1$ | $0$ | $1$ | $2$ || ---- | ---- | ---- | ---- | ---- | ---- || $f(x)$ | $a$ | $b$ | $c$ | $\\frac{1}{3}$ | $\\frac{1}{9}$ |$a=\\square$\n$b=\\square$\n$c=\\square$

Answer

Explanation:

Step1: Find $a$ (x=-2)

$f(-2) = \left(\frac{1}{3}\right)^{-2} = 3^2 = 9$

Step2: Find $b$ (x=-1)

$f(-1) = \left(\frac{1}{3}\right)^{-1} = 3^1 = 3$

Step3: Find $c$ (x=0)

$f(0) = \left(\frac{1}{3}\right)^0 = 1$

Answer:

$a=9$, $b=3$, $c=1$

Completed table:

$x$ $f(x)$
-2 9
-1 3
0 1
1 $\frac{1}{3}$
2 $\frac{1}{9}$