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

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Presentation transcript:

Functions

What is a function? Whenever one quantity depends on another Examples: Area of a circle depends on radius (A = πr 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) 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?

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

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

Examples Sketch each graph and find the domain and range 1) f(x) = 2x -1 2) g(x) = x 2

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.

2) The data shown comes from an experiment on the decay of an acid at 25 o C. 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. t02468 C(t)

3) A rectangular storage container with an open top has a volume of 10 m 3. The length of its base is twice its width. Material for the base costs $10 per m 2 and material for the sides costs $6 per m 2. Express the cost of materials as a function of the width of the base.

Homework Worksheet - Functions