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

Answer

Explanation:

Step1: Calculate (f(-2))

Substitute (x = - 2) into (f(x)=\left(\frac{1}{5}\right)^{x}). Using the rule (a^{-n}=\frac{1}{a^{n}}), we have (f(-2)=\left(\frac{1}{5}\right)^{-2}=5^{2}=25).

Step2: Calculate (f(-1))

Substitute (x=-1) into (f(x)=\left(\frac{1}{5}\right)^{x}). Using the rule (a^{-n}=\frac{1}{a^{n}}), we get (f(-1)=\left(\frac{1}{5}\right)^{-1}=5^{1} = 5).

Step3: Calculate (f(0))

Substitute (x = 0) into (f(x)=\left(\frac{1}{5}\right)^{x}). Using the rule (a^{0}=1(a\neq0)), we have (f(0)=\left(\frac{1}{5}\right)^{0}=1).

Step4: Calculate (f(1))

Substitute (x = 1) into (f(x)=\left(\frac{1}{5}\right)^{x}). We get (f(1)=\left(\frac{1}{5}\right)^{1}=\frac{1}{5}).

Step5: Calculate (f(2))

Substitute (x = 2) into (f(x)=\left(\frac{1}{5}\right)^{x}). We obtain (f(2)=\left(\frac{1}{5}\right)^{2}=\frac{1}{25}).

Answer:

The values of (f(x)) for (x=-2,-1,0,1,2) are (25,5,1,\frac{1}{5},\frac{1}{25}) respectively.