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Functions

Functions. What is a function?. Whenever one quantity depends on another Examples: Area of a circle depends on radius (A = π r 2 ) Population (P) depends on the time (t). Functions have sets which are real numbers. Domain – x values Range – y values – also denoted f(x)

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Functions

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  1. Functions

  2. What is a function? Whenever one quantity depends on another Examples: Area of a circle depends on radius (A = πr2) Population (P) depends on the time (t)

  3. Functions have sets which are real numbers Domain – x values Range – y values – also denoted f(x) Independent variable – represents number in the domain Dependent variable – number in the Range In the area equation, what is the independent and which is the dependent variable?

  4. Functions can be represented graphically y = f(x) Range Domain

  5. a) Find f(1) and f(5) b) what are the domain and range?

  6. Finding the Domain • Domain is all x values for which f(x) exists • Example: Find the domain for each below a) f(x) = √(5 – x2) b) g(x) = (x2 – x – 6)/(x2 – x)

  7. Functions can also be described in written form 1) When you turn on a hot water faucet, the temperature (T) depend on how long the water has been running. Draw a rough graph representing this.

  8. 2) The data shown comes from an experiment on the decay of an acid at 25oC. The concentration (C(t)) at different times, t, are given. Use the data to draw an approximation of the function. Use the graph to estimate the concentration after 5 minutes.

  9. 3) A rectangular storage container with an open top has a volume of 10 m3. The length of its base is twice its width. Material for the base costs $10 per m2 and material for the sides costs $6 per m2. Express the cost of materials as a function of the width of the base.

  10. Evaluating Functions • Functions can be evaluated at any point in their domain Example: For f(x) = 3x2 – x + 2, find: f(0) f(-1) f(2a) f(x + h) 2f(x)

  11. Sketch the function below and evaluate at f(0), f(1), and f(2) f(x) = 1 – x x ≤ 1 x2 x > 1

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