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\n( f(x)=left(\frac{1}{5}\right)^{x} )\n\nchoose which the graph of ( f(x)=left(\frac{1}{5}\right)^{x} ) below.\n\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\n( f(x)=left(\frac{1}{5}\right)^{x} )\n\nchoose which the graph of ( f(x)=left(\frac{1}{5}\right)^{x} ) below.\n\n

Answer

Explanation:

Step1: Calculate function values

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

Step2: Analyze the trend

As (x) increases ((-2\to - 1\to0\to1\to2)), (y = f(x)) values (25\to5\to1\to\frac{1}{5}\to\frac{1}{25}) are decreasing.

Answer:

The scatter - plot is a decreasing curve. As (x) increases, (y) values get smaller. For the function (y = b^{x}) with (0 < b<1), the graph approaches the (x) - axis ((y = 0)) as (x\to+\infty) and approaches (+\infty) as (x\to-\infty).