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D the set of positive integers divisible by 4

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Unformatted text preview: e options that cannot describe the graphs of the two functions. (E) The line shows a negative y-intercept (the point where the line crosses the vertical axis) and a negative slope less than –1 (that is, slightly more horizontal than a 45º angle). In 2 equation (E), − is the slope and –3 is the y3 intercept. Thus, equation (E) matches the graph of the function. 4. 270 Chapter 15 5. (E) The function h includes the two functional pairs (2,3) and (4,1). Since h is a linear function, its graph on the xy-plane is a straight line. You can determine the equation of the graph by first finding its slope (m): 1 − 3 −2 2 1 m = x − x = 4 − 2 = 2 = −1 . 2 1 y −y Exercise 8 1. (D) To solve this problem, consider each answer choice in turn, substituting the (x,y) pairs provided in the question for x and y in the equation. Among the five equations, only the equation in choice (D) holds for all four pairs. (A) The graph shows a parabola opening to the right with vertex at (–2,2). If the vertex were at the origin, the equation defining the parabola might be x = y2. Choices (D) and (E) define vertically oriented parabolas (in the general form y = x2) and thus can be eliminated. Considering the three remaining equations, (A) and (C) both hold for the (x,y) pair (–2,2), but (B) does not. Eliminate (B). Try substituting 0 for y in equations (A) and (C), and you’ll see that only in equation (A) is the corresponding x-value greater than 0, as the graph suggests. (E) The equation y = is a parabola with 3 vertex at the origin and opening upward. To see that this is the case, substitute some simple values for x and solve for y in each case. For example, substituting 0, 3, and –3 for x gives us the three (x,y) pairs (0,0), (3,3), and (–3,3). Plotting these three points on the xy-plane, then connecting them with a curved line, suffices to show a parabola with vertex (0,0) — opening upward. Choice (E) provides an equation x2 whose graph is identical to the...
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This note was uploaded on 08/15/2010 for the course MATH a4d4 taught by Professor Colon during the Spring '10 term at Embry-Riddle FL/AZ.

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