Question

graph the given function by making a table of coordinates. f(x)=2^x complete the table of coordinates. x -2 -1 0 1 2 y (type integers or fractions. simplify your answers.)

Explanation:

Step1: Substitute x = -2

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

Step2: Substitute x = -1

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

Step3: Substitute x = 0

Substitute \( x = 0 \) into \( f(x) = 2^x \). Using the exponent rule \( a^0 = 1 \) (for \( a
eq0 \)), we get \( 2^0 = 1 \).

Step4: Substitute x = 1

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

Step5: Substitute x = 2

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

Answer:

For \( x = -2 \), \( y=\frac{1}{4} \); for \( x = -1 \), \( y=\frac{1}{2} \); for \( x = 0 \), \( y = 1 \); for \( x = 1 \), \( y = 2 \); for \( x = 2 \), \( y = 4 \). So the completed table (from left to right in the y - column) has values \(\frac{1}{4}\), \(\frac{1}{2}\), \(1\), \(2\), \(4\).