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Holt Algebra Introduction to Functions 1-8 Introduction to Functions Holt Algebra 1 Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz

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Holt Algebra Introduction to Functions Warm Up Add. 1. Draw and label a number line. Then plot the points –2, 0, and 4. Evaluate each expression for the given value of x x + 1 for x = – x + 3 for x = 8 4. |x + 6| for x = –

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Holt Algebra Introduction to Functions Graph ordered pairs in the coordinate plane. Graph functions from ordered pairs. Objectives

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Holt Algebra Introduction to Functions coordinate plane axes origin x-axis y-axis ordered pair x-coordinate Vocabulary y-coordinate quadrant input output

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Holt Algebra Introduction to Functions The coordinate plane is formed by the intersection of two perpendicular number lines called axes. The point of intersection, called the origin, is at 0 on each number line. The horizontal number line is called the x-axis, and the vertical number line is called the y-axis.

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Holt Algebra Introduction to Functions Points on the coordinate plane are described using ordered pairs. An ordered pair consists of an x-coordinate and a y-coordinate and is written (x, y). Points are often named by a capital letter. The x-coordinate tells how many units to move left or right from the origin. The y-coordinate tells how many units to move up or down. Reading Math

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Holt Algebra Introduction to Functions Example 1: Graphing Points in the Coordinate Plane Graph each point. A. T(–4, 4) Start at the origin. Move 4 units left and 4 units up. B. U(0, –5) Start at the origin. Move 5 units down. T(–4, 4) U(0, –5) C. V (–2, –3) Start at the origin. Move 2 units left and 3 units down. V(–2, 3)

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Holt Algebra Introduction to Functions Check It Out! Example 1 Graph each point. A. R(2, – 3) B. S(0, 2) Start at the origin. Move 2 units right and 3 units down. Start at the origin. Move 2 units up. C. T( – 2, 6) Start at the origin. Move 2 units left and 6 units up. R(2, –3) S(0,2) T(–2,6)

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Holt Algebra Introduction to Functions Look at the graph at the top of this lesson. The axes divide the coordinate plane into four quadrants. Points that lie on an axis are not in any quadrant.

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Holt Algebra Introduction to Functions Example 2: Locating Points in the Coordinate Plane Name the quadrant in which each point lies. A. E Quadrant ll B. F no quadrant (y-axis) C. G Quadrant l D. H Quadrant lll E F H G x y

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Holt Algebra Introduction to Functions Name the quadrant in which each point lies. A. T no quadrant (y-axis) B. U Quadrant l C. V Quadrant lll D. W Quadrant ll Check It Out! Example 2 T W V U x y

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Holt Algebra Introduction to Functions An equation that contains two variables can be used as a rule to generate ordered pairs. When you substitute a value for x, you generate a value for y. The value substituted for x is called the input, and the value generated for y is called the output. y = 10x + 5 Output Input In a function, the value of y (the output) is determined by the value of x (the input). All of the equations in this lesson represent functions.

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Holt Algebra Introduction to Functions Example 3: Art Application An engraver charges a setup fee of $10 plus $2 for every word engraved. Write a rule for the engraver s fee. Write ordered pairs for the engraver s fee when there are 5, 10, 15, and 20 words engraved. Let y represent the engravers fee and x represent the number of words engraved. Engraver s feeis$10plus $2for each word y = · x y = x

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Holt Algebra Introduction to Functions The engravers fee is determined by the number of words in the engraving. So the number of words is the input and the engravers fee is the output. Writing Math

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Holt Algebra Introduction to Functions Example 3 Continued Number of Words Engraved RuleCharges Ordered Pair x (input)y = xy (output)(x, y) y = (5) 5 20 (5, 20) y = (10) 1030(10, 30) y = (15) (15, 40) y = (20) (20, 50)

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Holt Algebra Introduction to Functions Check It Out! Example 4 What if…? The caricature artist increased his fees. He now charges a $10 set up fee plus $20 for each person in the picture. Write a rule for the artists new fee. Find the artists fee when there are 1, 2, 3 and 4 people in the picture. y = x Let y represent the artists fee and x represent the number of people in the picture. Artist s feeis$10plus $20for each person y = · x

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Holt Algebra Introduction to Functions Number of People in Picture RuleCharges Ordered Pair x (input)y = xy (output)(x, y) y = (1) 1 30 (1, 30) y = (2) 250(2, 50) y = (3) 3 70 (3, 70) y = (4) 490 (4, 90) Check It Out! Example 4 Continued

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Holt Algebra Introduction to Functions When you graph ordered pairs generated by a function, they may create a pattern.

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Holt Algebra Introduction to Functions Example 4A: Generating and Graphing Ordered Pairs Generate ordered pairs for the function using the given values for x. Graph the ordered pairs and describe the pattern. y = 2x + 1; x = –2, –1, 0, 1, 2 –2–2 –1– ( – 2) + 1 = – 3 ( – 2, – 3) ( – 1, – 1) (0, 1) (1, 3) (2, 5) 2( – 1) + 1 = – 1 2(0) + 1 = 1 2(1) + 1 = 3 2(2) + 1 = 5 InputOutput Ordered Pair xy(x, y) The points form a line.

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Holt Algebra Introduction to Functions Example 4B: Generating and Graphing Ordered Pairs y = x 2 – 3; x = – 2, – 1, 0, 1, 2 –2–2 –1– ( – 2) 2 – 3 = 1 ( – 2, 1) ( – 1, –2) (0, – 3) (1, – 2) (2, 1) ( – 1) 2 – 3 = – 2 (0) 2 – 3 = – 3 (1) 2 – 3 = – 2 (2) 2 – 3 = 1 InputOutput Ordered Pair xy(x, y) The points form a U shape.

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Holt Algebra Introduction to Functions Example 4C: Generating and Graphing Ordered Pairs y = |x – 2|; x = 0, 1, 2, 3, |0 – 2| = 2 (0, 2) (1, 1) (2, 0) (3, 1) (4, 2) |1 – 2| = 1 |2 – 2| = 0 |3 – 2| = 1 |4 – 2| = 2 InputOutput Ordered Pair xy(x, y) The points form a V shape.

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Holt Algebra Introduction to Functions –4–4 –2– – 2 – 4 = – 6 ( – 4, – 6) ( – 2, – 5) (0, – 4) (2, – 3) (4, – 2) – 1 – 4 = – 5 0 – 4 = – 4 1 – 4 = – 3 2 – 4 = – 2 InputOutput Ordered Pair xy(x, y) The points form a line. Check It Out! Example 4a y = x – 4; x = –4, –2, 0, 2,

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Holt Algebra Introduction to Functions –3–3 –1– ( – 3) = 30 (–3, 30) (–1, 6) (0, 3) (1, 6) (3, 30) 3( – 1) = 6 3(0) = 3 3(1) = 6 3(3) = 30 InputOutput Ordered Pair xy(x, y) The points form a U shape. Check It Out! Example 4b y = 3x 2 + 3; x = – 3, – 1, 0, 1, 3

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Holt Algebra Introduction to Functions |0 – 2| = 2 (0, 2) (1, 1) (2, 0) (3, 1) (4, 2) |1 – 2| = 1 |2 – 2| = 0 |3 – 2| = 1 |4 – 2| = 2 InputOutput Ordered Pair xy(x, y) The points form a V shape. Check It Out! Example 4c y = |x – 2|; x = 0, 1, 2, 3, 4

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Holt Algebra Introduction to Functions Lesson Quiz: Part 1 Graph each point. Name the quadrant in which each point lies. 1. (2, 0) 2. (–3, –4) 3. (1, –1) 4. (–5, 4) None lll lV ll

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Holt Algebra Introduction to Functions Lesson Quiz: Part 2 5. A cable company charges $50 to set up a movie channel and $3.00 per movie watched. Write a rule for the companys fee. Write ordered pairs for the fee when a person watches 1, 2, 3, or 4 movies. y = x; (1, 53), (2, 56), (3, 59), (4, 62)

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Holt Algebra Introduction to Functions Lesson Quiz: Part 3 6. Generate ordered pairs for y = x² –5 using x = –2, –1, 0, 1, and 2. Graph the ordered pairs, and describe the pattern. (–2, –1) (–1, –4) (0, –5) (1, –4) (2, –1) The pattern is U-shaped.

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