In coordinate geometry, an ordered pair is represented as (x,y)
The ordered pairs on [tex]f(x) = (\frac 14)^x[/tex] are (-1,4) and (3,1/64)
The function is given as:
[tex]f(x) = (\frac 14)^x[/tex]
A. (1,4)
This means that;
f(1) =4, where x = 1
So, we have:
[tex]f(x) = (\frac 14)^x[/tex]
[tex]f(1) = (\frac 14)^1[/tex]
[tex]f(1) = \frac 14[/tex]
Option (a) is false:
B. (-1,4)
This means that;
f(-1) =4, where x = -1
So, we have:
[tex]f(x) = (\frac 14)^x[/tex]
[tex]f(-1) = (\frac 14)^{-1[/tex]
Apply law of indices
[tex]f(-1) = (4)^1[/tex]
[tex]f(-1) = 4[/tex]
Option (b) is true:
C. (3,1/64)
This means that;
f(3) =1/64, where x = 3
So, we have:
[tex]f(x) = (\frac 14)^x[/tex]
[tex]f(3) = (\frac 14)^3[/tex]
[tex]f(3) = \frac 1{64}[/tex]
Option (c) is true:
D. (0,1/4)
This means that;
f(0) =1/4, where x = 0
So, we have:
[tex]f(x) = (\frac 14)^x[/tex]
[tex]f(0) = (\frac 14)^0[/tex]
[tex]f(0) = 1[/tex]
Option (d) is false:
Read more about ordered pairs at:
https://brainly.com/question/13688667
