Answer: The correct options are
(B) (-1, 10)
(C) (0, 7)
(E) (2, 1).
Step-by-step explanation: We are given to select all the points that lie on the graph of the following function :
[tex]f(x)=7-3x~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
Option (A) : (x, f(x)) = (-2, 1).
We have
[tex]f(-2)=7-3\times(-2)=7+6=13\neq 1.[/tex]
So, the point (-2, 1) does not lie on the graph of equation (i).
Option (A) is incorrect.
Option (B) : (x, f(x)) = (-1, 10).
We have
[tex]f(-1)=7-3\times(-1)=7+3=10.[/tex]
So, the point (-2, 1) lie on the graph of equation (i).
Option (B) is correct.
Option (C) : (x, f(x)) = (0, 7).
We have
[tex]f(0)=7-3\times0=7-0=7.[/tex]
So, the point (0, 7) lie on the graph of equation (i).
Option (C) is correct.
Option (D) : (x, f(x)) = (1, 5).
We have
[tex]f(1)=7-3\times1=7-3=4\neq 5.[/tex]
So, the point (1, 5) does not lie on the graph of equation (i).
Option (D) is incorrect.
Option (E) : (x, f(x)) = (2, 1).
We have
[tex]f(2)=7-3\times(2)=7-6=1.[/tex]
So, the point (2, 1) lie on the graph of equation (i).
Option (E) is correct.
Thus, options (B), (C) and (E) are correct.
