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## 1-8

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**1-8**Introduction to Functions Holt Algebra 1 Warm Up Lesson Presentation Lesson Quiz**-**- - - - - 6 5 4 3 2 1 0 1 2 3 4 5 6 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. 2. 2x + 1 for x = 3 7 1 4 1 – x + 3 for x = 8 3. 4 4. |x + 6| for x = –10**Objectives**Graph ordered pairs in the coordinate plane. Graph functions from ordered pairs.**Vocabulary**coordinate plane axes origin x-axis y-axis ordered pair x-coordinate y-coordinate quadrant input output**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.**Reading Math**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. 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.**U(0, –5)**• Example 1: Graphing Points in the Coordinate Plane Graph each point. A. T(–4, 4) Start at the origin. T(–4, 4) • Move 4 units left and 4 units up. B. U(0, –5) Start at the origin. Move 5 units down. • C. V (–2, –3) V(–2, −3) Start at the origin. Move 2 units left and 3 units down.**Check It Out! Example 1**Graph each point. A. R(2, –3) Start at the origin. T(–2,6) Move 2 units right and 3 units down. S(0,2) B. S(0, 2) Start at the origin. Move 2 units up. C. T(–2, 6) • R(2, –3) Start at the origin. Move 2 units left and 6 units up.**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.**•F**•E •G •H Example 2: Locating Points in the Coordinate Plane Name the quadrant in which each point lies. y A. E Quadrant ll B. F no quadrant (y-axis) x C.G Quadrant l D.H Quadrant lll**Check It Out! Example 2**Name the quadrant in which each point lies. y A. T •U •W no quadrant (y-axis) •T B. U Quadrant l x C.V Quadrant lll •V D.W Quadrant ll**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. Output Input y= 10x + 5 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.**Engraver’s fee**is $10 plus word $2 for each y 10 x = + 2 · 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 engraver’s fee and x represent the number of words engraved. y = 10 + 2x**Writing Math**The engraver’s fee is determined by the number of words in the engraving. So the number of words is the input and the engraver’s fee is the output.**Example 3 Continued**5 y = 10 + 2(5) 20 (5, 20) 10 30 (10, 30) y = 10 + 2(10) y = 10 + 2(15) 15 (15, 40) 40 20 50 y = 10 + 2(20) (20, 50)**Artist’s fee**is $10 plus person $20 for each y 10 x = + 20 · 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 artist’s new fee. Find the artist’s fee when there are 1, 2, 3 and 4 people in the picture. Let y represent the artist’s fee and x represent the number of people in the picture. y = 10 + 20x**Check It Out! Example 4 Continued**1 y = 10 + 20(1) 30 (1, 30) 2 50 (2, 50) y = 10 + 20(2) y = 10 + 20(3) 3 (3, 70) 70 4 90 y = 10 + 20(4) (4, 90)**When you graph ordered pairs generated by a function, they**may create a pattern.**•**• • • • 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, –3) –2 2(–2)+ 1 = –3 2(–1)+ 1 = –1 (–1, –1) –1 2(0)+ 1 = 1 (0, 1) 0 2(1) + 1 = 3 1 (1, 3) 2(2) + 1 = 5 (2, 5) 2 The points form a line.**Example 4B: Generating and Graphing Ordered Pairs**y = x2– 3; x = –2, –1, 0, 1, 2 (–2, 1) –2 (–2)2– 3 = 1 (–1)2– 3 = –2 –1 (–1, –2) (0)2– 3 = –3 (0, –3) 0 (1)2– 3 = –2 1 (1, –2) (2)2– 3 = 1 (2, 1) 2 The points form a U shape.**Example 4C: Generating and Graphing Ordered Pairs**y = |x –2|; x = 0, 1, 2, 3, 4 0 (0, 2) |0– 2| = 2 |1– 2| = 1 1 (1, 1) |2– 2| = 0 (2, 0) 2 |3– 2| = 1 3 (3, 1) (4, 2) 4 |4– 2| = 2 The points form a V shape.**1**2 Check It Out! Example 4a y = x – 4; x = –4, –2, 0, 2, 4 (–4, –6) –4 –2 – 4 = –6 –2 –1 – 4 = –5 (–2, –5) 0 – 4 = –4 (0, –4) 0 1 – 4 = –3 2 (2, –3) 4 2 – 4 = –2 (4, –2) The points form a line.**Check It Out! Example 4b**y = 3x2 + 3; x = –3, –1, 0, 1, 3 (–3, 30) –3 3(–3)2+ 3 = 30 3(–1)2+ 3 = 6 –1 (–1, 6) 3(0)2+ 3 = 3 (0, 3) 0 3(1)2+ 3 = 6 1 (1, 6) 3(3)2+ 3 = 30 (3, 30) 3 The points form a U shape.**Check It Out! Example 4c**y = |x– 2|; x = 0, 1, 2, 3, 4 0 (0, 2) |0– 2| = 2 |1– 2| = 1 1 (1, 1) |2– 2| = 0 (2, 0) 2 |3– 2| = 1 3 (3, 1) (4, 2) 4 |4– 2| = 2 The points form a V shape.**Lesson Quiz: Part 1**Graph each point. Name the quadrant in which each point lies. 1. (2, 0) None 2. (–3, –4) lll • 3. (1, –1) lV • • 4. (–5, 4) ll •**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 company’s fee. Write ordered pairs for the fee when a person watches 1, 2, 3, or 4 movies. y = 50 + 3x; (1, 53), (2, 56), (3, 59), (4, 62)**•**• • • • 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.