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.\nf(x) = (\\frac{1}{5})^{x}\nfor each value of x, find the corresponding value for f(x).\n\n\nchoose which the graph of f(x) = (\\frac{1}{5})^{x} below

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.\nf(x) = (\\frac{1}{5})^{x}\nfor each value of x, find the corresponding value for f(x).\n\n\nchoose which the graph of f(x) = (\\frac{1}{5})^{x} below

Answer

Explanation:

Step1: Substitute (x = - 2)

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

Step2: Substitute (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)), so (f(0)=\left(\frac{1}{5}\right)^{0}=1)

Step4: Substitute (x = 1)

(f(1)=\left(\frac{1}{5}\right)^{1}=\frac{1}{5})

Step5: Substitute (x = 2)

(f(2)=\left(\frac{1}{5}\right)^{2}=\frac{1}{25})

Answer:

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

The shape of the scatter - plot (and the graph of (y = b^{x},0 < b<1)) is a curve that falls from left to right. It approaches the (x) - axis as (x\to\infty) and rises without bound as (x\to-\infty).