Question

graph the given function by making a table of coordinates. \\( f(x) = 3^x \\) complete the table of coordinates. \\( \

$$\begin{array}{|c|c|} \\hline x & y \\\\ \\hline -2 & \\frac{1}{9} \\\\ \\hline -1 & \\frac{1}{3} \\\\ \\hline 0 & 1 \\\\ \\hline 1 & 3 \\\\ \\hline 2 & 9 \\\\ \\hline \\end{array}$$

\\) (type integers or fractions. simplify your answers.) choose the correct graph below. \\( \circ \\) a. graph a \\( \circ \\) b. graph b \\( \circ \\) c. graph c \\( \circ \\) d. graph d

Explanation:

Step1: Calculate \( y = f(x)=3^{x} \) for \( x=-2 \)

Substitute \( x = - 2 \) into \( y = 3^{x} \), we get \( y=3^{-2}=\frac{1}{3^{2}}=\frac{1}{9} \)

Step2: Calculate \( y = f(x)=3^{x} \) for \( x=-1 \)

Substitute \( x=-1 \) into \( y = 3^{x} \), we get \( y = 3^{-1}=\frac{1}{3^{1}}=\frac{1}{3} \)

Step3: Calculate \( y = f(x)=3^{x} \) for \( x = 0 \)

Substitute \( x = 0 \) into \( y = 3^{x} \), we get \( y=3^{0}=1 \) (since \( a^{0}=1,a
eq0 \))

Step4: Calculate \( y = f(x)=3^{x} \) for \( x = 1 \)

Substitute \( x = 1 \) into \( y = 3^{x} \), we get \( y=3^{1}=3 \)

Step5: Calculate \( y = f(x)=3^{x} \) for \( x = 2 \)

Substitute \( x = 2 \) into \( y = 3^{x} \), we get \( y=3^{2}=9 \)

The completed table is:

\( x\)	\( y = 3^{x}\)
\(-1\)	\(\frac{1}{3}\)
\(0\)	\(1\)
\(1\)	\(3\)
\(2\)	\(9\)

For the graph, when \( x=-2,y=\frac{1}{9}\approx0.11 \); \( x = - 1,y=\frac{1}{3}\approx0.33 \); \( x=0,y = 1 \); \( x = 1,y=3 \); \( x=2,y = 9 \). The function \( y = 3^{x}\) is an exponential growth function (\(a = 3>1\) in \(y=a^{x}\)).

Answer:

The completed table:

\( x\)	\( y = 3^{x}\)
\(-1\)	\(\frac{1}{3}\)
\(0\)	\(1\)
\(1\)	\(3\)
\(2\)	\(9\)

Since the problem of choosing the graph is not fully clear (assuming standard axes where \(x\)-axis and \(y\)-axis are properly labeled and the points \((-2,\frac{1}{9}),(-1,\frac{1}{3}),(0,1),(1,3),(2,9)\) are plotted on a graph with \(y = 3^{x}\) being an increasing curve (exponential growth). If we assume the \(x\)-axis and \(y\)-axis are in a standard orientation (horizontal \(x\), vertical \(y\)), the graph which has points passing through \((0,1)\) (y - intercept of exponential function \(y=a^{x}\) is \((0,1)\)) and is increasing is the correct one.