2.8

Functions

9 flashcards to master Functions

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Definition Flip

What is a function? Define it in terms of input and output.

Answer Flip

A function is a relationship between a set of inputs (the domain) and a set of permissible outputs (the range) with the property that each input is related to exactly one output.

Example: f(x) = x + 2 is a function where each input 'x' produces only one output.
Key Concept Flip

Explain function notation and provide an example.

Answer Flip

Function notation is a way of writing functions that clearly indicates the input and output. It uses the form f(x), where 'f' is the function name and 'x' is the input.

Example: If f(x) = 3x - 1, then f(2) = 3(2) - 1 = 5.
Key Concept Flip

If f(x) = 2x + 1 and g(x) = x^2, find the composite function f(g(x)).

Answer Flip

To find f(g(x)), substitute g(x) into f(x). So, f(g(x)) = f(x^2) = 2(x^2) + 1 = 2x^2 + 1. Therefore, f(g(x)) = 2x^2 + 1.

Definition Flip

What is the domain of a function?

Answer Flip

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Example: if f(x) = 1/x, the domain is all real numbers except x = 0.
Definition Flip

What is the range of a function?

Answer Flip

The range of a function is the set of all possible output values (y-values) that the function can produce. It represents the values that f(x) can take.

Example: if f(x) = x^2, the range is all non-negative real numbers.
Key Concept Flip

Explain what an inverse function is and its relationship to the original function.

Answer Flip

An inverse function, denoted f⁻¹(x), 'undoes' the original function f(x). If f(a) = b, then f⁻¹(b) = a. The domain of f(x) is the range of f⁻¹(x), and vice-versa.

Key Concept Flip

Find the inverse function of f(x) = x - 5.

Answer Flip

To find the inverse, let y = x - 5. Swap x and y: x = y - 5. Solve for y: y = x + 5. Thus, f⁻¹(x) = x + 5.

Key Concept Flip

Given the function f(x) = √(x - 2), state its domain.

Answer Flip

For the square root function to be defined, the expression inside the square root must be non-negative. So, x - 2 ≥ 0, which means x ≥ 2. Therefore, the domain is x ≥ 2.

Key Concept Flip

Describe how to determine if a graph represents a function.

Answer Flip

Use the vertical line test. If any vertical line intersects the graph at more than one point, the graph does not represent a function. This is because a single x-value would correspond to multiple y-values.

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2.7 Straight line graphs 2.9 Differentiation

Key Questions: Functions

What is a function? Define it in terms of input and output.

A function is a relationship between a set of inputs (the domain) and a set of permissible outputs (the range) with the property that each input is related to exactly one output.

Example: f(x) = x + 2 is a function where each input 'x' produces only one output.
What is the domain of a function?

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Example: if f(x) = 1/x, the domain is all real numbers except x = 0.
What is the range of a function?

The range of a function is the set of all possible output values (y-values) that the function can produce. It represents the values that f(x) can take.

Example: if f(x) = x^2, the range is all non-negative real numbers.

About Functions (2.8)

These 9 flashcards cover everything you need to know about Functions for your Cambridge IGCSE Mathematics (0580) exam. Each card is designed based on the official syllabus requirements.

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