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)=left(\frac{7}{12}\right)^{x}, g(x)=left(\frac{12}{7}\right)^{x} \n\nall graphs are displayed in a (-5,5,1) by (-12,12,1) viewing window.\n\nthe domain of ( f(x) ) is ( (-infty,infty) ) and the domain 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 interval notation.)\n\nthe graph of ( f(x) ) has a factor of. the graph of ( g(x) ) has a factor of \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)=left(\frac{7}{12}\right)^{x}, g(x)=left(\frac{12}{7}\right)^{x} \n\nall graphs are displayed in a (-5,5,1) by (-12,12,1) viewing window.\n\nthe domain of ( f(x) ) is ( (-infty,infty) ) and the domain 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 interval notation.)\n\nthe graph of ( f(x) ) has a factor of. the graph of ( g(x) ) has a factor of \n\n(type integers or fractions.)

Answer

Explanation:

Step1: Analyze the base of the exponential function

For an exponential function (y = a^x), if (0 < a< 1), it is a decay function; if (a > 1), it is an increasing function. For (f(x)=\left(\frac{7}{12}\right)^x), since (0<\frac{7}{12}<1), (f(x)) is a decay function. The base (a = \frac{7}{12}) is the decay factor. For (g(x)=\left(\frac{12}{7}\right)^x), since (\frac{12}{7}>1), (g(x)) is an increasing function. The base (a=\frac{12}{7}) is the growth factor.

Answer:

The graph of (f(x)) has a decay factor of (\frac{7}{12}). The graph of (g(x)) has a growth factor of (\frac{12}{7}).