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Warm Up

Warm Up. Find the equation of a line with slope of 4 passing through the point (-1, 6). James is driving at an average speed of 60 miles per hour. He wanted to record his trip but he forgot to start until he was 30 miles into his trip. Write a model to represent his trip.

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Warm Up

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  1. Warm Up • Find the equation of a line with slope of 4 passing through the point (-1, 6). • James is driving at an average speed of 60 miles per hour. He wanted to record his trip but he forgot to start until he was 30 miles into his trip. Write a model to represent his trip.

  2. Characteristics of Functions

  3. Standards and Learning Targets • F.IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. • SWBAT determine the domain and range of a function. • SWBAT determine the x and y intercepts of a linear function • SWBAT determine whether a linear function is increasing or decreasing • SWBAT determine the rate of change of a function

  4. Domain and Range • Discrete Graphs: you just LIST the domain and range. • Continuous Graphs: you use INTERVAL NOTATION (#, #): are used when there is an open dot or the number is NOT included on the graph. [#, #] are used when there is a closed dot or when the number is included on the graph.

  5. Quick Check!

  6. Intercepts (aka “zeros”) • x-intercept – the point at which the line intersects the x-axis at (x, 0) • y-intercept – the point at which the line intersects the y-axis at (0, y) ZEROS are the same thing as the x-intercepts

  7. Example 1: Finding the Zeros (x-intercepts)

  8. Example 2: Find the y-intercept

  9. Increasing/Decreasing Behavior Move left to right • If your finger is moving UP then the function is increasing • If your finger is moving DOWN then the function is decreasing • If your finder isn’t moving up or down, than your function is CONSTANT

  10. Quick Check!

  11. Rate of Change • Rate of Change is the average amount of change in her y-values. • Rate of Change is essentially the SLOPE.

  12. Example: Rate of Change with Points • Find the rate of change, given the following points: (2,3) and (1,4)

  13. Example: Rate of Change with functions Find the average rate of change for f(x) = ½x + 4 from [0,3]

  14. Guided Practice

  15. Independent Classwork

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