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Understanding Functions in Algebra II Honors

Learn about functions, function notation, domain, and range in Algebra II Honors. Discover how to determine if a relation is a function, evaluate functions, and identify domain and range from equations or graphs.

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Understanding Functions in Algebra II Honors

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  1. Algebra II Honors—Day 8

  2. Goals for Today • Reminder—First Graded Homework Assignment (checked for accuracy)—due next Tuesday, Sept. 10 • Essential Questions • New Material • Classwork/Homework

  3. Essential Questions • What is a function and how do I determine if a relation is a function? • How do I use function notation to evaluate a function? • How do I determine a function’s domain and range from its equation or from its graph?

  4. Notes • A function is a relation that maps every x-value with exactly one y-value. • In other words, if I tell you the x, you will always know the y based on the function definition. • Vertical line test helps identify graphs as functions or not.

  5. Functions • Functions: {(3,6), (4, 22), (-8, 20), (6.5, 20)}—none of the x-values repeat. Each x is paired with only one y. Notice that it’s OK for the y-values to repeat. This is a function because if you tell me what x is, you will get a unique value of y by plugging in the value of x. This is a linear function.

  6. Practice • Function Notation Classwork

  7. Domain and Range • Domain—consists of all possible inputs for a function (the x-values or the independent variable values) • Range—all of the outcomes that are possible for the given domain • Some functions have limited domains and ranges. • You will need to learn how to recognize domains and ranges from graphs.

  8. Examples • For linear equations: • Domain is all real numbers • D: • Range is all real numbers • R: This means that a line goes on and on forever. Every value of x gives a unique value of y, and every value of x and y are possible.

  9. Domain and Range from Graphs • Sometimes the domain and range are determined from the graph based only on what you see. • On this graph, the domain is (-3,3) and the range is (-9,0). Why????

  10. Homework • Domain and Range Handout—due tomorrow • Problems 1, 2, 3, 4, 7, 10, 11, 14 • Quotable Puzzles—due Monday

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