Question

graph the given function by making a table of coordinates.\\( f(x) = 2^x \\)\
complete the table of coordinates.\
\\(\

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

\\)\
(type integers or fractions. simplify your answers.)

Explanation:

Step1: For \( x = -2 \)

Substitute \( x = -2 \) into \( f(x) = 2^x \). Using the rule \( a^{-n}=\frac{1}{a^n} \), we have \( 2^{-2}=\frac{1}{2^2}=\frac{1}{4} \).

Step2: For \( x = -1 \)

Substitute \( x = -1 \) into \( f(x) = 2^x \). Using \( a^{-n}=\frac{1}{a^n} \), \( 2^{-1}=\frac{1}{2^1}=\frac{1}{2} \).

Step3: For \( x = 0 \)

Substitute \( x = 0 \) into \( f(x) = 2^x \). By the rule \( a^0 = 1 \) ( \( a
eq0 \) ), \( 2^0 = 1 \).

Step4: For \( x = 1 \)

Substitute \( x = 1 \) into \( f(x) = 2^x \). So \( 2^1 = 2 \).

Step5: For \( x = 2 \)

Substitute \( x = 2 \) into \( f(x) = 2^x \). Then \( 2^2 = 4 \).

Answer:

When \( x=-2 \), \( y = \frac{1}{4} \); when \( x = -1 \), \( y=\frac{1}{2} \); when \( x = 0 \), \( y = 1 \); when \( x = 1 \), \( y = 2 \); when \( x = 2 \), \( y = 4 \). So the completed table (from \( x=-2 \) to \( x = 2 \)) has \( y \)-values \( \frac{1}{4},\frac{1}{2},1,2,4 \) respectively.