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UNIT 2 1.7, 4.8 Introduction to Functions

UNIT 2 1.7, 4.8 Introduction to Functions. HW: 1.7 12 – 24 m3, 26 4.8 11 – 22 function : A rule that relates two numbers called the input and output. For every input there is exactly one output. Examples. 1.7, 4.8Introduction to Functions Definitions.

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UNIT 2 1.7, 4.8 Introduction to Functions

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  1. UNIT 21.7, 4.8 Introduction to Functions HW: 1.7 12 – 24 m3, 26 4.8 11 – 22 function: A rule that relates two numbers called the input and output. For every input there is exactly one output. Examples

  2. 1.7, 4.8Introduction to FunctionsDefinitions input: a number entered into a function. (DOMAIN) output: the result of entering a number into a function. (RANGE) domain: the collection of all input values for a function (the x-values) range: the collection of all output values for a function (the y-values and )

  3. 1.7, 4.8 Introduction to Functions Make an input-output table for the function below. Use 1, 2, 3, 4, and 5 as the domain: Domain Range

  4. 1.7, 4.8 Introduction to Functions Make an input-output table for the function below. Use 1, 2, 3, 4, and 5 as the domain: Domain Range

  5. 1.7, 4.8 Introduction to Functions Solution a. Is a function. For every ONE input there is a unique OUTPUT. Domain: Range: Solution “b” Is a NOT a function. The input {1} has two different outputs {5, 7}.

  6. 1.7, 4.8 Introduction to Functions

  7. 1.7, 4.8 Introduction to FunctionsPractice Decide whether the graph represents y as a function of x. If yes, then state the domain and range.

  8. Unit 24.3 Quick graph (x, y intercepts)4.6 Quick graph (slope-intercept) Homework (due Monday) • 4.3 15 – 54 m3 no 33 • 4.6 24 – 45 m3 • Use any method to graph. Ignore the directions. • Two lines per coordinate plane.

  9. 4.3 Quick graph (x, y intercepts)4.6 Quick graph (slope-intercept) • Which method to use depends on how the problem looks when given to you. • Use x, y intercepts • Use slope-intercept

  10. Method #2Quick graph using x, y intercepts • Make an x, y T-table • Make x = 0 and solve for y. (y – intercept) • Make y = 0 and solve for x.(x – intercept) • Plot the two intercepts and draw the line.

  11. Examples

  12. 4.6 Graphing lines using the slope and y-intercept • Slope intercept Form Slopey – intercept – starting point on the Y- axis Directions to the next point

  13. 4.6 Graphing y = mx + b

  14. Graph using any method

  15. UNIT 2 4.4 The slope of a line5.1 writing a linear equation. Homework 4.4 21 – 41 odd 5.1 12 – 22 even write all equations in Slope - intercept form and Standard form Slope Slope -intercept Standard

  16. FINDING THE SLOPE OF A LINE (x1,y1) (x1,y1) y (x2,y2) (x2,y2) (x2, y2) (x1, y1) (y2 - y1) (x2 - x1) x rise change in y = x2-x1 run change in x y2-y1 The slope m of the nonvertical line passing through the points(x1, y1) and(x2, y2)is Read y1 as “y sub one” Read x1 as “x sub one” m = =

  17. Examples

  18. Examples Find the slope of the line passing through the given points. x, y x, y

  19. 4.4 practice

  20. 5.1 Writing linear equations • Slope intercept form • Standard form • are integers • Given the slope and the y – intercept , simply substitute slope – intercept form. • Rewrite the equation into Standard form.

  21. E.g. Write in slope - intercept form 1) m = 4and b = 1 slope – intercept form standard form You will have TWO answers. 5.1 writing linear equations given slope and y - intercept

  22. 5.1 • Slope = and the y – intercept = -4 slope – intercept form standard form

  23. Unit 25.2, 5.3 writing linear equations Homework 5.2 12 – 33 m3 5.3from power point Write all equations in slope – intercept form and standard form and

  24. 5.3 homeworkGive your self 5 spaces per problem Write a linear equation in slope – intercept form and standard form.

  25. 5.2 writing linear equations given slope and a point

  26. Point – slope form E.g. Distribute slope intercept form standard form

  27. m = 2, ( 5, 15) m = 3, ( 2, -6) m = , ( -8, 4) m = -2, ( -3, 8) m = , ( 9, -1) 5.2 writing linear equations given slope and a point

  28. 5.3 writing linear equations given two points. • Step 1 • Find slope m = • Step 2 • Substitute m and one of the given points into point – slope form

  29. 5.3 writing linear equations given two points. • (5, 8), (7, 12) • (2, 4), (3, 7) • (-1, 8), (2, 2)

  30. m = 3, (1, 8) m = -1, (2, 4) m = 4, (-1, 3) m = -5, (7, -2) m = , (4, 7) m = -4, (-3, -7) m = 1, (0, -6) m = , (3, -5) Cw 5.2Write an equation of a line.

  31. Hw 5.2, 5.3 Power point Write an equation of a line. • (1,6),(4,12) • (4,2),(5,5) • (-2,4),(1,1) • (0,10),(4,2)

  32. Write a linear equation in the form y = mx + b

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