Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN: 9781305071742
Author: James Stewart, Lothar Redlin, Saleem Watson
Publisher: Cengage Learning
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Question
Chapter C, Problem 2E
To determine
The most appropriate graph of the equation
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(a) Graph f(x) = 2x and g(x) = 12 on the same Cartesian plane.(b) Shade the region bounded by the y-axis, f(x) = 2x , and g(x) = 12 on the graph drawn in part (a).(c) Solve f(x) = g(x) and label the point of intersection on the graph drawn in part (a).
0<x<2pi
F(x)=-4cosx
G(x)=2cosx+3
graph f(x) and g(x) on the same coordinate system for 0<x<2pi and solve f(x)=g(x) on [0,2pi] and label point of intersection on the graph (both x and y values)
(a) Graph f1x2 = 3-x+1
and g1x2 = 3x-2
on the same
Cartesian plane.(b) Shade the region bounded by the y-axis, f1x2 = 3-x+1,
and g1x2 = 3x-2
on the graph drawn in part (a).(c) Solve f1x2 = g1x2 and label the point of intersectionon the graph drawn in part (a).
Chapter C Solutions
Algebra and Trigonometry (MindTap Course List)
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Similar questions
- Suppose we want to graph an equation in x and y. a If we replace x by x3, the graph of the equation is shifted to the _____ by 3 units. If we replace x by x+3, the graph of the equation is shifted to the ____ by 3 units. b If we replace y by y1, the graph of the equation is shifted ______ by 1 unit. If we replace y by y+1, the graph of the equation is shifted _______ by 1 unitarrow_forwardThe graph of y=f(x) contains the point (-5,2) what point must lie on the graph resulting in: a. If the graph is reflected about the y axsis b. If the graph is reflected about the x axsis c. If the graph is translated up 4 units d. If the graph is reflected about the x a sis then shifted down by 2 units e. If the graph is horizontally stretched by a factor of 2 f. f(-x)-2 g. -f(x+2) h. 0.5f(x) i. 3f(0.25x) j. f(x+1)+3arrow_forwardThe graph of a function f is given. The x y-coordinate plane is given. A curve with 3 parts is graphed. The first part is linear, enters the window in the second quadrant, goes down and right, crosses the x-axis at approximately x = −0.33, crosses the y-axis at y = −0.25, and ends at the open point (1, −1). The second part is the point (1, 1). The third part is linear, begins at the open point (1, −1), goes up and right, crosses the x-axis at x = 2, and exits the window in the first quadrant. Determine whether f is continuous on its domain. continuous not continuous If it is not continuous on its domain, say why. lim x→1+ f(x) ≠ lim x→1− f(x), so lim x→1 f(x) does not exist. The function is not defined at x = 1. The graph is continuous on its domain. lim x→1 f(x) = −1 ≠ f(1)arrow_forward
- x) Consider the graphs of y1 = f(x) and y2 = f(2x + 7). Make a prediction about how these graphs are related. In particular what does the graph of y2 = f(2x + 7) look like in comparison to y1 = f(x)? y) Suppose that, in addition, we know that f(x) = x2. Graph y1 = f(x) and y2 = f(2x + 7). Make sure you measure the horizontal distance between the vertices of the two graphs. How do your findings fit with your expectations from part a)? z) When we graph y = Af(Bx + C) + D, based on our knowledge of the graph of y = f(x) and assuming that A, B, C and D are constants, does the order in which we carry out the four transformations matter? What order would you recommend?arrow_forwardWorld Population A low-projection scenario forworld population for 1995–2150 by the United Nationsis given by the function y = -0.36x2 + 38.52x +5822.86, where x is the number of years after 1990and the world population is measured in millions ofpeople.a. Find the input and output at the vertex of thegraph of this model.b. Interpret the values from part (a).c. For what years after 1995 does this model predictthat the population will increase?arrow_forward(a) Graph f(x) = 2x+1and g(x) = 2-x+2on the sameCartesian plane.(b) Shade the region bounded by the y-axis, f(x) = 2x+1,and g(x) = 2-x+2on the graph drawn in part (a).(c) Solve f(x) = g(x) and label the point of intersectionon the graph drawn in part (a).arrow_forward
- 5. For y=x2 -x, the graph is given (a) mark two points on the graph, one with x1=3 and one with x2=3+Δx b) draw a segment representing Δx (the change in x) and label it (c) find the expression for its length (d) draw a segment representing Δy (tharrow_forwardFGH has vertices F (-2,1) , G(-2,4) and H (0,2) . Graph FGH . Then reflect it across the X-axis and translate it 3 units downarrow_forward
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