graph the exponential function.\n\n$f(x)=(\\frac{5}{4})^{x}$\n\nplot five points on the graph of the…

graph the exponential function.\n\n$f(x)=(\\frac{5}{4})^{x}$\n\nplot five points on the graph of the function, and also draw the asymptote. then click on the graph - a - function button.

graph the exponential function.\n\n$f(x)=(\\frac{5}{4})^{x}$\n\nplot five points on the graph of the function, and also draw the asymptote. then click on the graph - a - function button.

Answer

Explanation:

Step1: Identify function type and asymptote

Exponential function with base ( \frac{5}{4} > 1 ), horizontal asymptote at ( y = 0 ).

Step2: Calculate points for ( x = -2, -1, 0, 1, 2 )

For ( x = -2 ): ( f(-2) = \left(\frac{5}{4}\right)^{-2} = \left(\frac{4}{5}\right)^2 = \frac{16}{25} )
For ( x = -1 ): ( f(-1) = \left(\frac{5}{4}\right)^{-1} = \frac{4}{5} )
For ( x = 0 ): ( f(0) = \left(\frac{5}{4}\right)^0 = 1 )
For ( x = 1 ): ( f(1) = \frac{5}{4} )
For ( x = 2 ): ( f(2) = \left(\frac{5}{4}\right)^2 = \frac{25}{16} )

Step3: List coordinates and asymptote

Points: ( (-2, \frac{16}{25}) ), ( (-1, \frac{4}{5}) ), ( (0, 1) ), ( (1, \frac{5}{4}) ), ( (2, \frac{25}{16}) ); Asymptote: ( y = 0 ).

Answer:

Points to plot: ( (-2, \frac{16}{25}) ), ( (-1, \frac{4}{5}) ), ( (0, 1) ), ( (1, \frac{5}{4}) ), ( (2, \frac{25}{16}) ); Asymptote: ( y = 0 ) (x-axis).