graph the exponential function.\n$f(x)=\\left(\\frac{4}{3}\\right)^x$\nplot five points on the graph of the…

graph the exponential function.\n$f(x)=\\left(\\frac{4}{3}\\right)^x$\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$f(x)=\\left(\\frac{4}{3}\\right)^x$\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: Find the y - intercept

When (x = 0), (f(0)=\left(\frac{4}{3}\right)^0=1). So the point is ((0,1)).

Step2: Find a point for (x = 1)

When (x = 1), (f(1)=\frac{4}{3}\approx1.33). So the point is ((1,\frac{4}{3})).

Step3: Find a point for (x = 2)

When (x = 2), (f(2)=\left(\frac{4}{3}\right)^2=\frac{16}{9}\approx1.78). So the point is ((2,\frac{16}{9})).

Step4: Find a point for (x=- 1)

When (x=-1), (f(-1)=\left(\frac{4}{3}\right)^{-1}=\frac{3}{4} = 0.75). So the point is ((-1,\frac{3}{4})).

Step5: Find a point for (x=-2)

When (x=-2), (f(-2)=\left(\frac{4}{3}\right)^{-2}=\frac{9}{16}=0.5625). So the point is ((-2,\frac{9}{16})). The horizontal asymptote of the exponential function (y = a^x) ((a>0,a\neq1)) is (y = 0).

Answer:

The five points are ((0,1)), ((1,\frac{4}{3})), ((2,\frac{16}{9})), ((-1,\frac{3}{4})), ((-2,\frac{9}{16})) and the horizontal asymptote is (y = 0).