PRE-CALCULUS FOR ALL
FINAL PROJECT (MAT 115)
LECTURER: Dr. Oh
STUDENT NAME:
, CHAPTER ONE
FUNCTION
1.1 DEFINITION OF ONE TO ONE FUNCTION
One to one functions are functions where each input corresponds to only one
unique output, and two inputs cannot give the same outputs.
EXAMPLE 1.1
Considering the function 𝑓(𝑥) = 2𝑥 + 3, find 𝑓(1), 𝑓(2) and 𝑓(3)
SOLUTION
Substituting the corresponding value of 𝑥 into the function,
𝑓(1) = 2(1) + 3 = 5
𝑓(2) = 2(2) + 3 = 7
𝑓(3) = 2(3) + 3 = 9
It can be seen that each inputted value has a different output making it a One-
to-One function.
COMMON ERROR: One common mistake is mistakenly thinking that if a
function gives a distinct output value for each inputted value, then it is
automatically one-to-one.
FINAL PROJECT (MAT 115)
LECTURER: Dr. Oh
STUDENT NAME:
, CHAPTER ONE
FUNCTION
1.1 DEFINITION OF ONE TO ONE FUNCTION
One to one functions are functions where each input corresponds to only one
unique output, and two inputs cannot give the same outputs.
EXAMPLE 1.1
Considering the function 𝑓(𝑥) = 2𝑥 + 3, find 𝑓(1), 𝑓(2) and 𝑓(3)
SOLUTION
Substituting the corresponding value of 𝑥 into the function,
𝑓(1) = 2(1) + 3 = 5
𝑓(2) = 2(2) + 3 = 7
𝑓(3) = 2(3) + 3 = 9
It can be seen that each inputted value has a different output making it a One-
to-One function.
COMMON ERROR: One common mistake is mistakenly thinking that if a
function gives a distinct output value for each inputted value, then it is
automatically one-to-one.
