Question

use - 2, - 1, 0, 1, and 2 for x and find the corresponding values of f(x) for the following exponential function. then, choose which graph represents the exponential function.

f(x)=2^{(x + 1)}

Explanation:

Step1: Calculate \( f(x) \) for \( x = - 2 \)

Substitute \( x=-2 \) into \( f(x)=2^{(x + 1)} \).
\( f(-2)=2^{-2 + 1}=2^{-1}=\frac{1}{2} \)

Step2: Calculate \( f(x) \) for \( x=-1 \)

Substitute \( x = - 1 \) into \( f(x)=2^{(x + 1)} \).
\( f(-1)=2^{-1+1}=2^{0}=1 \)

Step3: Calculate \( f(x) \) for \( x = 0 \)

Substitute \( x = 0 \) into \( f(x)=2^{(x + 1)} \).
\( f(0)=2^{0 + 1}=2^{1}=2 \)

Step4: Calculate \( f(x) \) for \( x = 1 \)

Substitute \( x = 1 \) into \( f(x)=2^{(x + 1)} \).
\( f(1)=2^{1+1}=2^{2}=4 \)

Step5: Calculate \( f(x) \) for \( x = 2 \)

Substitute \( x = 2 \) into \( f(x)=2^{(x + 1)} \).
\( f(2)=2^{2+1}=2^{3}=8 \)

Since the function \( y = 2^{x+1} \) is an exponential growth function (base \( a = 2>1 \)), as \( x \) increases, \( y \) increases.

Answer:

B.