Respuesta :
Answer:
(0,1) and (-2,9)
Step-by-step explanation:
A point (x,y) lies on the graph of f(x) = [tex](\frac{1}{3} )^{x}[/tex] if it satisfies the condition y = [tex](\frac{1}{3} )^{x}[/tex]
(0,1):
x = 0 and y = 1.
This point satisfies the required condition as
[tex](\frac{1}{3} )^{0}[/tex] = 1
Hence, this point is on the graph of f(x) = [tex](\frac{1}{3} )^{x}[/tex]
(3,27):
x = 3 and y = 27.
This point doesn't satisfy the required condition as
[tex](\frac{1}{3} )^{3}[/tex] = [tex]\frac{1}{27}[/tex] ≠ 27
Hence, this point is not on the graph of f(x) = [tex](\frac{1}{3} )^{x}[/tex]
(-2,9):
x = -2 and y = 9.
This point satisfies the required condition as
[tex](\frac{1}{3} )^{-2}[/tex] = [tex]3^{2}[/tex] = 9
Hence, this point is on the graph of f(x) = [tex](\frac{1}{3} )^{x}[/tex]
(-1,[tex]-\frac{1}{3}[/tex]):
x = -1 and y = [tex]-\frac{1}{3}[/tex].
This point satisfies the required condition as
y = [tex](\frac{1}{3} )^{-1}[/tex] = [tex]3^{1}[/tex] = 3 ≠ [tex]-\frac{1}{3}[/tex]
Hence, this point is not on the graph of f(x) = [tex](\frac{1}{3} )^{x}[/tex]
