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Functions

Functions. Function Notation. f(x) is a fancy way of saying ____. Why use function notation?. How can we tell if a relation between two variables represents a function?. Every value for _____ must yield _______ _____ value for _____.

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Functions

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  1. Functions

  2. Function Notation • f(x) is a fancy way of saying ____. • Why use function notation?

  3. How can we tell if a relation between two variables represents a function? • Every value for _____ must yield _______ _____ value for _____. • Does the relation (0, 1), (1, 2), (2, 2), (3, 4) represent a function? • Does the relation (0, 1), (0, 2), (1, 3), (2, 4) represent a function?

  4. Checking graphically? • Vertical Line Test: If you can draw a vertical line through any part of the graph and it hits at _____ _____ ____ place, the graph does not represent a function. • Is a function? • Is a function?

  5. Domain • The domain of a function tells us what values can be entered for _____ to give a real number solution. • Types of problems that cause a restriction on the domain: • Fractions • Square Roots • Real World Problems

  6. Examples (Give domain of each function) 1) 2) 3) The price for a prom ticket is $60 and the cost for running the prom is $8,000. Write a function that relates the number of tickets sold, x, to the profit P(x) and give the domain.

  7. Range • The range of a function tells us all of the possible real solutions that we could get for ____. • Types of Problems that cause restrictions on the range: • Fractions • Square Roots • Absolute Values & Even powered polynomials • Real World Problems

  8. Examples(Give the range for each function) 1) 2) 3) 4) Find the range of the Prom problem

  9. Zeros of a Function • The zeros of a function are the values for x that make the value of the function (or “y”) equal to zero • Zeros are also called: • Roots • X-intercepts • Solutions

  10. Examples(Find the zeros of each function) 1) 2)

  11. Find the domain, range, and zeros of each of the following functions 1) 2) 3) 4)

  12. Practice • Pg. 122 ( 1 – 15 odd)

  13. Step Functions • A cell phone company charges $20/month for service and $1 for every minute or fraction of a minute over the plan. • What is the lowest payment you could have with this company? • What would your monthly cost be if you talked for 4.5 minutes over the plan?

  14. Piecewise Functions • Sketch the graph for Then, give the domain , range, and zeros.

  15. Piecewise Functions (Ex2) Graph and give the domain, range and zeros

  16. Ex3) Graph and give the domain, range and zeros

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