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Functions

Maths: Edexcel IGCSE Higher, topic 3.2.1

Functions

A function takes an element of one set and maps it to an element in another set.

Writing functions

Writing functions

  • We can write the function that doubles a number and then adds 3 in these ways.
If x 2, f(x) 7

If x = 2, f(x) = 7

If x 10, f(x) 23

If x = 10, f(x) = 23

If x -2, f(x) -1

If x = -2, f(x) = -1

If x 0, f(x) 3

If x = 0, f(x) = 3

Domain and Range

A function is a relation in which each possible input value leads to exactly one output value.

Domain

Domain

  • The input values make up the domain.
  • The domain of the function f(x) = x2 is all of the numbers from -∞ to +∞.
Range

Range

  • The output values make up the range.
  • The range of the function f(x) = x2 are all of the positive numbers and 0.
Allowed values

Allowed values

  • Certain functions are not defined for certain inputs.
  • f(x)=1xf(x)=\frac{1}{x} is not defined for x=0x=0 as f(0)=∞f(0) = \infty.
  • f(x)=xf(x) = \sqrt{x} is not defined for x<0x<0.

Test yourself on Functions

  • Which of these are acceptable notations for a function?

  • Which number is NOT in the domain of the function f(x)=1x+6f(x) = \frac{1}{x + 6}

  • Which number is NOT in the domain of the function f(x)=12x+6f(x) = \frac{1}{2x + 6}

  • Which number is NOT in the domain of the function f(x)=2xf(x) =\sqrt{2x}

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