Question

graph the given function by making a table of coordinates.
$f(x) = \left( \frac{1}{3} \
ight)^x$

complete the table of coordinates.

x	-2	-1	0	1	2
y	\square	\square	\square	\square	\square

(type integers or fractions. simplify your answers.)

Explanation:

Step1: Substitute \(x = - 2\)

Use the formula \(a^{-n}=\frac{1}{a^{n}}\) and \((\frac{a}{b})^{-n}=(\frac{b}{a})^{n}\).
When \(x=-2\), \(y = (\frac{1}{3})^{-2}=3^{2}=9\)

Step2: Substitute \(x=-1\)

When \(x = - 1\), \(y=(\frac{1}{3})^{-1}=3^{1}=3\)

Step3: Substitute \(x = 0\)

Use the formula \(a^{0}=1(a
eq0)\).
When \(x = 0\), \(y=(\frac{1}{3})^{0}=1\)

Step4: Substitute \(x = 1\)

When \(x = 1\), \(y=(\frac{1}{3})^{1}=\frac{1}{3}\)

Step5: Substitute \(x = 2\)

When \(x = 2\), \(y=(\frac{1}{3})^{2}=\frac{1}{9}\)

Answer:

\(x\)	\(-2\)	\(-1\)	\(0\)	\(1\)	\(2\)