Injective, Surjective & Bijective Functions (Leaving Cert Mathematics): Quizzes

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Injective, Surjective & Bijective Functions
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What does it mean for a function to be injective?

Different inputs give different outputs

Which condition defines an injective function?

f(x1)=f(x2)  ⟹  x1=x2f(x_1) = f(x_2) \implies x_1 = x_2

How does an injective function pass the horizontal line test?

Horizontal line intersects at most once

Is y=x2y = x^2 over R\mathbb{R} an injective function?

No

What does it mean for a function to be surjective?

Every codomain element is mapped to

For a surjective function, what equals the codomain?

The range

Is f(x)=x2:R→[0,∞)f(x) = x^2: \mathbb{R} \to [0, \infty) surjective?

Yes

Why is f(x)=x2:R→Rf(x) = x^2: \mathbb{R} \to \mathbb{R} NOT surjective?

Negative values aren't reached

What does it mean for a function to be bijective?

Both injective and surjective

What special property do bijective functions have?

They have inverse functions

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Injective, Surjective & Bijective Functions

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Fundamentals of Functions

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Graph Transformations

Injective, Surjective & Bijective Functions

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Inverse Functions

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Fundamentals of Functions

The Basics

Types of Graphs

Graph Transformations

Injective, Surjective & Bijective Functions

Composite Functions

Inverse Functions

Explore Leaving Cert Mathematics Exam Questions by Topics

Fundamentals of Functions

The Basics

Types of Graphs

Graph Transformations

Injective, Surjective & Bijective Functions

Composite Functions

Inverse Functions

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