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Core 3 Functions 1

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Designed for OCR A Level mathematics.

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Starter Sketch the graphs of a) b) b) a)
Objective: to identify the domain and range of functions and begin to use function notation
This is the graph of a function as there is only one value of y for each value of x.
This is NOT the graph of a function as there are two or three values of y for some values of x.
Domain and Range The set of numbers x for which a function y = f(x) is defined is called the domain of the function. The set of numbers y for which a function y = f(x) is defined is called the range of the function. Domain: Range:
Function Notation This means f is the function whose domain is the set of real numbers which turns any input x into the output 2x – 10. This means g is the function whose domain is the set of real numbers excluding 2 which turns any input x into the output 3 ÷ (x – 2).
Core 3 & 4 Textbook Exercise 2B Page 26 Questions 1, 2, 3, 4, 9
Plenary The functions f and g are defined as follows: Given that f(2) = 11 and the graph of g is a tangent to the graph of f at the point where x = 1, find the values of A, B and C. Hence, state the range of f.

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Core 3 Functions 1

  • 1. Starter Sketch the graphs of a) b) b) a)
  • 2. Objective: to identify the domain and range of functions and begin to use function notation
  • 3. This is the graph of a function as there is only one value of y for each value of x.
  • 4. This is NOT the graph of a function as there are two or three values of y for some values of x.
  • 5. Domain and Range The set of numbers x for which a function y = f(x) is defined is called the domain of the function. The set of numbers y for which a function y = f(x) is defined is called the range of the function. Domain: Range:
  • 6. Function Notation This means f is the function whose domain is the set of real numbers which turns any input x into the output 2x – 10. This means g is the function whose domain is the set of real numbers excluding 2 which turns any input x into the output 3 ÷ (x – 2).
  • 7. Core 3 & 4 Textbook Exercise 2B Page 26 Questions 1, 2, 3, 4, 9
  • 8. Plenary The functions f and g are defined as follows: Given that f(2) = 11 and the graph of g is a tangent to the graph of f at the point where x = 1, find the values of A, B and C. Hence, state the range of f.