[tex](-1, 9), \ (0, 6), \ (1, 4), \ (2, 2\frac{2}{3} ), \ (1, \frac{7}{9} )[/tex]
Solution:
Given [tex]f(x)=6\left(\frac{2}{3}\right)^{x}[/tex]
Domain = {–1, 0, 1, 2, 3}
Substitute the given values in the function.
At x = –1,
[tex]f(-1)=6\left(\frac{2}{3}\right)^{-1}[/tex]
[tex]=6 \times \frac{3}{2}[/tex]
= 9
[tex](x, f(x))=(-1, 9)[/tex]
At x = –0,
[tex]f(0)=6\left(\frac{2}{3}\right)^{0}=6[/tex]
[tex](x, f(x))=(0,6)[/tex]
At x = 1,
[tex]f(1)=6\left(\frac{2}{3}\right)^{1}=4[/tex]
[tex](x, f(x))=(1,4)[/tex]
At x = 2,
[tex]f(2)=6\left(\frac{2}{3}\right)^{2}[/tex]
[tex]=\frac{24}{9}[/tex]
[tex]=2\frac{6}{9}[/tex] (Cancel the common terms)
[tex]=2\frac{2}{3}[/tex]
[tex](x, f(x))=(2, 2\frac{2}{3} )[/tex]
At x = 3,
[tex]f(3)=6\left(\frac{2}{3}\right)^{3}[/tex]
[tex]=\frac{48}{27}[/tex] (Cancel the common terms)
[tex]=\frac{16}{9}[/tex]
[tex]=1\frac{7}{9}[/tex]
[tex](x, f(x))=(3, 1\frac{7}{9} )[/tex]
Plot the points in the graph.
The image of the graph is attached below.
