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Warm Up #6 Evaluate each expression for the given value of x.
1. x2 + 5x; x = –2 2. 4x – 3x3; x = 2 –6 ANSWER ANSWER –16
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EXAMPLE 1 Represent relations Consider the relation given by the ordered pair (–2, –3), (–1, 1), (1, 3), (2, –2), and (3, 1). a. Identify the domain and range. SOLUTION The domain consists of all the x-coordinates: –2, –1, 1, 2, and The range consists of all the y-coordinates: –3, –2, 1, and 3.
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EXAMPLE 1 Represent relations Represent the relation using a graph and a mapping diagram. b. (–2, –3), (–1, 1), (1, 3), (2, –2), and (3, 1). SOLUTION b. Graph Mapping Diagram
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EXAMPLE 2 Identify functions Tell whether the relation is a function. Explain. a. SOLUTION The relation is a function because each input is mapped onto exactly one output.
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EXAMPLE 2 Identify functions Tell whether the relation is a function. Explain. b. SOLUTION The relation is not a function because the input 1 is mapped onto both – 1 and 2.
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GUIDED PRACTICE for Examples 1 and 2 1. Consider the relation given by the ordered pairs (–4, 3), (–2, 1), (0, 3), (1, –2), and (–2, –4) a. Identify the domain and range. SOLUTION The domain consists of all the x-coordinates: –4, –2, 0 and 1, The range consists of all the y-coordinates: 3, 1, –2 and –4
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GUIDED PRACTICE for Examples 1 and 2 b. Represent the relation using a table and a mapping diagram. Consider the relation given by the ordered pair (–4, 3), (–2, 1), (0, 3), (1, –2), and (-2, -4). SOLUTION
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GUIDED PRACTICE for Examples 1 and 2 2. Tell whether the relation is a function. Explain. ANSWER Yes; each input has exactly one output.
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EXAMPLE 2 Standardized Test Practice SOLUTION Let (x1, y1) = (–1, 3) and (x2, y2) = (2, –1). m = y2 – y1 x2 – x1 = – 1 – 3 2 – (–1) = 4 3 ANSWER The correct answer is A.
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GUIDED PRACTICE for Examples 1 and 2 (7, 3), (– 1, 7) SOLUTION Let (x1, y1) = (7, 3) and (x2, y2) = (– 1, 7). m = y2 – y1 x2 – x1 = 7 – 3 – 1 – 7 = 1 2 – ANSWER 1 2 –
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Classify lines using slope
EXAMPLE 3 Classify lines using slope Without graphing, tell whether the line through the given points rises, falls, is horizontal, or is vertical. a. (– 5, 1), (3, 1) b. (– 6, 0), (2, –4) c. (–1, 3), (5, 8) d. (4, 6), (4, –1) SOLUTION 1 – 1 3– (–5) = m = a. 8 = 0 Because m = 0, the line is horizontal. – 4 – 0 2– (–6) = m = b. – 4 8 = 1 2 – Because m < 0, the line falls.
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Classify lines using slope
EXAMPLE 3 Classify lines using slope Without graphing, tell whether the line through the given points rises, falls, is horizontal, or is vertical. a. (– 5, 1), (3, 1) b. (– 6, 0), (2, –4) c. (–1, 3), (5, 8) d. (4, 6), (4, –1) SOLUTION 1 – 1 3– (–5) = m = a. 8 = 0 Because m = 0, the line is horizontal. – 4 – 0 2– (–6) = m = b. – 4 8 = 1 2 – Because m < 0, the line falls.
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a. b. EXAMPLE 4 Classify parallel and perpendicular lines
Tell whether the lines are parallel, perpendicular, or neither. Line 1: through (– 2, 2) and (0, – 1) a. Line 2: through (– 4, – 1) and (2, 3) Line 1: through (1, 2) and (4, – 3) b. Line 2: through (– 4, 3) and (– 1, – 2) SOLUTION Find the slopes of the two lines. a. m1 = –1 – 2 0 – (– 2) = – 3 2 3 2 –
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EXAMPLE 4 Classify parallel and perpendicular lines m2 = 3 – (– 1) 2 – (– 4) = 4 6 2 3 ANSWER Because m1m2 = – 2 3 = – 1, m1 and m2 are negative reciprocals of each other. So, the lines are perpendicular.
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EXAMPLE 4 Classify parallel and perpendicular lines Find the slopes of the two lines. b. m1 = –3 – 2 4 – 1 = – 5 3 = 5 3 – m2 = – 2 – 3 – 1 – (– 4) = – 5 3 = 5 3 – ANSWER Because m1 = m2 (and the lines are different), you can conclude that the lines are parallel.
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Classwork Assignment WS 2-1 (1-11, all) WS 2-2 (1-21 odd)
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