Unformatted text preview: is the slope of the graph of f(x) = − 1 x. You obtain this slope by substituting –4x 2 3: x≈ 1 for x in the function: f(–4x) = − 2 (–4x) = 2x. 8. = 4π r 2 − π r 2 = 3π r 2 (E) Substitute the variable expression given in each answer choice, in turn, for x in the x function f(x) = –2x2 + 2. Substituting − 2 (given in choice E) for x yields the equation 2 y=− x +2:
4 f − x = ( −2 ) − x 2 2 Drawing a line segment from C to O forms two right triangles, each with hypotenuse 2r. Since OC = r, by the Pythagorean Theorem, the ratios among the triangle’s sides are 1: 3 :2, with corresponding angle ratios 90°:60°:30°. ∠A and ∠B each = 30°. Accordingly, interior ∠AOB measures 120°, or one third the degree measure of the circle. Hence, the area of the shaded region is two thirds of area A and must equal 2πr2. 4. (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 45° angle). In 2 equation (E), − is the slope and –3 is the y3 intercept. Thus, equation (E) matches the graph of the line. (B) Points (5,–2) and (–3,3) are two points on line b. The slope of b is the change in the ycoordinates divided by the corresponding change in the x-coordinate:
mb = 3 − (−2) 5 5 = , or − −3 − 5 −8 8 () () 2 2 + 2 = ( −2 ) x + 2 = 4 2 2 − 2 x + 2, or − x + 2 4 8 The graph of y = − x 2 4 is a downward opening parabola with vertex at the origin (0,0). The figure shows the graph of that equation, except translated 2 units up. To confirm that (E) is the correct choice, substitute the (x,y) pairs (–4,–2) and (4,–2), which are shown in the graph, for x and y in the equation y = − x + 2 , and you’ll
2 find that the equation holds for both value pairs. 9. The correct answer is 6. By multiplying the number of chickens by the number of eggs they lay per week, then adding together the products, you can find the number of eggs laid by...
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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.
- Spring '10