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

graph the exponential function.\n\n$f(x)=4(\\frac{5}{4})^{x}$\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$f(x)=4(\\frac{5}{4})^{x}$\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 at ( x = 0 )

( f(0) = 4\left(\frac{5}{4}\right)^0 = 4 \times 1 = 4 ), point: ( (0, 4) )

Step3: Calculate points at ( x = 1 )

( f(1) = 4\left(\frac{5}{4}\right)^1 = 4 \times \frac{5}{4} = 5 ), point: ( (1, 5) )

Step4: Calculate points at ( x = -1 )

( f(-1) = 4\left(\frac{5}{4}\right)^{-1} = 4 \times \frac{4}{5} = \frac{16}{5} = 3.2 ), point: ( (-1, 3.2) )

Step5: Calculate points at ( x = 2 )

( f(2) = 4\left(\frac{5}{4}\right)^2 = 4 \times \frac{25}{16} = \frac{25}{4} = 6.25 ), point: ( (2, 6.25) )

Step6: Calculate points at ( x = -2 )

( f(-2) = 4\left(\frac{5}{4}\right)^{-2} = 4 \times \frac{16}{25} = \frac{64}{25} = 2.56 ), point: ( (-2, 2.56) )

Answer:

Points: ( (0, 4) ), ( (1, 5) ), ( (-1, 3.2) ), ( (2, 6.25) ), ( (-2, 2.56) ); Asymptote: ( y = 0 )