use a table of coordinates to graph the exponential function. begin by selecting - 2, - 1, 0, 1, and 2 for…

use a table of coordinates to graph the exponential function. begin by selecting - 2, - 1, 0, 1, and 2 for x. based on your graph, describe the shape of a scatter plot that can be modeled by $f(x)=b^{x}$, $0 < b < 1$.\n$f(x)=(\\frac{1}{5})^{x}$\nfor each value of x, find the corresponding value for $f(x)$.\n

use a table of coordinates to graph the exponential function. begin by selecting - 2, - 1, 0, 1, and 2 for x. based on your graph, describe the shape of a scatter plot that can be modeled by $f(x)=b^{x}$, $0 < b < 1$.\n$f(x)=(\\frac{1}{5})^{x}$\nfor each value of x, find the corresponding value for $f(x)$.\n

Answer

Explanation:

Step1: Substitute (x = - 2)

Use the formula (a^{-n}=\frac{1}{a^{n}}) and (a^{n}=\frac{1}{a^{-n}}). When (x=-2), (f(-2)=\left(\frac{1}{5}\right)^{-2}=5^{2} = 25)

Step2: Substitute (x=-1)

When (x = - 1), (f(-1)=\left(\frac{1}{5}\right)^{-1}=5^{1}=5)

Step3: Substitute (x = 0)

Use the rule (a^{0}=1(a\neq0)). When (x = 0), (f(0)=\left(\frac{1}{5}\right)^{0}=1)

Step4: Substitute (x = 1)

When (x = 1), (f(1)=\left(\frac{1}{5}\right)^{1}=\frac{1}{5}=0.2)

Step5: Substitute (x = 2)

When (x = 2), (f(2)=\left(\frac{1}{5}\right)^{2}=\frac{1}{25}=0.04)

Answer:

(x) (-2) (-1) (0) (1) (2)
(f(x)=\left(\frac{1}{5}\right)^{x}) (25) (5) (1) (0.2) (0.04)