Which of the following are one-to-one functions?

Question

1. 
   
2. F={(−1,−4),(0,0),(3,1),(6,4),(8,7),(10,13)}
3. M={(−2,0),(2,3),(2,4),(6,8),(7,−6),(11,16)}
4. R={(−4,−1),(3,2),(5,6),(9,7),(10,13),(16,15)}
5. S={(9,−8),(0,−6),(6,2),(5,3),(7,4),(3,6)}
6. G={(7,2),(10,−2),(−3,0),(6,1),(−1,−2),(1,2)}

Answer 1

F, R, & S are one to one functions

M is not a function due to (2,3) and (2,4).

M fails the vertical line test

plot the points, if you can draw a vertical line and intersect 2 points, it's not a function

a vertical line, x=2, intersects 2 points: (2,3) and (2,4)

G is a function but not one to one due to (10,-2) and (1,-2)

G fails the horizontal line test

plot the points, if a horizontal line intersects 2 points, it's not a one-to-one function

a horizontal line, y=-2, intersects 2 points: (10,-2) and (1,-2)

Answer 2