Worksheet: Bijective, Injective, and Surjective Functions

In this worksheet, we will practice identifying bijective, injective, and surjective functions.

Q1:

Which curve among those shown in the graph below is a one-to-one function?

  • Athe red one
  • Bthe orange one
  • Cthe blue one
  • Dthe green one

Q2:

Which of the following functions is one-to-one and onto from to ?

  • A𝑓(𝑥)=2𝑥1
  • B𝑓(𝑥)=3𝑥7
  • C𝑓(𝑥)=𝑒
  • D𝑓(𝑥)=1𝑥

Q3:

Which of the following is true about a one-to-one function?

  • AIt does not have an inverse.
  • BIt is always increasing or decreasing.
  • CIt has an inverse.
  • DIt is its own inverse.

Q4:

Let 𝑓: be given by 𝑓(𝑛)=𝑛1. What is true about 𝑓?

  • A𝑓 is a bijection.
  • B𝑓 is not defined.
  • C𝑓 is onto.
  • D𝑓 is one-to-one.

Q5:

Is the function shown in the graph a one-to-one function?

  • Ayes
  • Bno

Q6:

Is the function shown in the graph a one-to-one function?

  • Ayes
  • Bno

Q7:

Is the function shown in the graph a one-to-one function?

  • Ayes
  • Bno

Q8:

Is the function shown in the graph a one-to-one function?

  • Ano
  • Byes

Q9:

Which of the following is a one-to-one function?

  • A𝑓(𝑥)=𝑥cos
  • B𝑓(𝑥)=𝑥
  • C𝑓(𝑥)=𝑥
  • D𝑓(𝑥)=𝑥+𝑥

Q10:

Which of the following is a one-to-one function?

  • A𝑓(𝑥)=𝑥
  • B𝑓(𝑥)=𝑥+2
  • C𝑓(𝑥)=|𝑥|
  • D𝑓(𝑥)=5

Q11:

Which of the following is a bijection from to ?

  • A𝑓(𝑥)=1𝑥
  • B𝑓(𝑥)=𝑒
  • C𝑓(𝑥)=2𝑥1
  • D𝑓(𝑥)=2𝑥

Q12:

Which of the following is true about 𝑓:?

  • AImage of 𝑓=.
  • B𝑓 cannot be one-to-one.
  • C𝑓 can be a bijection.
  • D𝑓 cannot be onto.

Q13:

Suppose 𝑓: given by 𝑓𝑝𝑞=𝑝. What is the most that can be said about 𝑓?

  • A𝑓 is onto
  • B𝑓 has an inverse
  • C𝑓 is well-defined
  • D𝑓 is one-to-one

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