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)=5^{(x - 1)}
now, choose which graph represents ( f(x)=5^{(x - 1)} )

Explanation:

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

Substitute \(x=-2\) into \(f(x)=5^{(x - 1)}\), we get \(f(-2)=5^{(-2 - 1)}=5^{-3}=\frac{1}{5^{3}}=\frac{1}{125}=0.008\)

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

Substitute \(x = - 1\) into \(f(x)=5^{(x - 1)}\), we get \(f(-1)=5^{(-1 - 1)}=5^{-2}=\frac{1}{5^{2}}=\frac{1}{25}=0.04\)

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

Substitute \(x = 0\) into \(f(x)=5^{(x - 1)}\), we get \(f(0)=5^{(0 - 1)}=5^{-1}=\frac{1}{5}=0.2\)

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

Substitute \(x = 1\) into \(f(x)=5^{(x - 1)}\), we get \(f(1)=5^{(1 - 1)}=5^{0}=1\)

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

Substitute \(x = 2\) into \(f(x)=5^{(x - 1)}\), we get \(f(2)=5^{(2 - 1)}=5^{1}=5\)

Since the function \(y = 5^{(x - 1)}\) is an exponential growth function (\(a = 5>1\)). When \(x = 1\), \(y = 1\). As \(x\) increases, \(y\) increases rapidly and as \(x\) decreases, \(y\) approaches \(0\)

Answer:

B.