using your graphing calculator, investigate the graphs of the following family (group) of functions…

using your graphing calculator, investigate the graphs of the following family (group) of functions. describe any relationships within the family, including domain and range, growth or decay factors, vertical and horizontal intercepts, and asymptotes. identify the functions as increasing or decreasing.\n\n$f(x)=9^{x},g(x)=(\\frac {1}{9})^{x}$\n\nall graphs are displayed - 12,12,1 viewing window.\n\nthe domain of $f(x)$ is $(-$ decay main of $g(x)$ is $(-\\infty,\\infty)$. the range of $f(x)$ is $(0,\\infty)$ and the range of $g(x)$ is $(0,\\infty)$.\n\n(type your answer in int growth\n\nthe graph of $f(x)$ has a factor of $\\square$. the graph of $g(x)$ has a factor of $\\square$.\n\n(type integers or fractions.)

using your graphing calculator, investigate the graphs of the following family (group) of functions. describe any relationships within the family, including domain and range, growth or decay factors, vertical and horizontal intercepts, and asymptotes. identify the functions as increasing or decreasing.\n\n$f(x)=9^{x},g(x)=(\\frac {1}{9})^{x}$\n\nall graphs are displayed - 12,12,1 viewing window.\n\nthe domain of $f(x)$ is $(-$ decay main of $g(x)$ is $(-\\infty,\\infty)$. the range of $f(x)$ is $(0,\\infty)$ and the range of $g(x)$ is $(0,\\infty)$.\n\n(type your answer in int growth\n\nthe graph of $f(x)$ has a factor of $\\square$. the graph of $g(x)$ has a factor of $\\square$.\n\n(type integers or fractions.)

Answer

Explanation:

Step1: Analyze (f(x) = 9^{x})

For an exponential function (y = a^{x}) ((a>0,a\neq1)), when (a = 9>1), it is an exponential growth function. The general form of an exponential function is (y=a^{x}), and the growth - factor is (a). So for (f(x)=9^{x}), the growth factor is (9).

Step2: Analyze (g(x)=\left(\frac{1}{9}\right)^{x})

We know that (y = a^{x}), when (0 < a<1), it is an exponential decay function. We can rewrite (g(x)=\left(\frac{1}{9}\right)^{x}=9^{-x}). The decay - factor formula for (y = a^{x}(0 < a<1)) is (a). So for (g(x)=\left(\frac{1}{9}\right)^{x}), the decay factor is (\frac{1}{9}).

Answer:

The graph of (f(x)) has a growth factor of (9). The graph of (g(x)) has a decay factor of (\frac{1}{9}).