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Keishiro Ueki 31 oktTo graph y = 1 2f(x) y = 1 2 f ( x) , start with the graph of f(x) f ( x) and adjust the y y coordinates to half their original values Since the original graph consists of lines, it suffices toGraphs of y=f(x) and y=f(x) Below is the graph of , where a is the value in the sliderChange the values of a and check what happens to the graph of f(x)
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Is addition and one when it is subtraction x^ {2}yxy^ {2}=43 x 2 y x y 2 = 4 3 Subtract 43Using the binomial coefficients, the above formula can be written as (x y)n = (n 0)xn (n 1)xn − 1y (n 2)xn − 2y2 (n k)xn − kyk (n n)yn where (n k) = n!Figure 1572 Double change of variable At this point we are twothirds done with the task we know the r θ limits of integration, and we can easily convert the function to the new variables √x2 y2 = √r2cos2θ r2sin2θ = r√cos2θ sin2θ = r The final, and most difficult, task is to figure out what replaces dxdy
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slope yintercept ↓ ↓ y = x 2 The yintercept is where the line crosses the yaxis So which ever graph has 2 as the yintercept in correctIts more complex when the graphs have the same intercept but in this case this should be easy to find So looking at the graphs you can see that the 3rd graph is the correct answerGraph y=x^21 (label the vertex and the axis of symmetry) and tell whether the parabola opens upward or downward y=x^21 This is a parabola that opens upwards with vertex at (0,1) Graph the parabola, y =x^21 by finding the turning point and using a table to find values for x and y
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Solve the following system of equations graphically y 4 = 0 2x y 2 = 0 What is the solution set?To solve it graphically you probably have to draw a graph I'll do the rest of it 2 x y = 6 2 x − y = − 2 These are easily solved simultaneously, by adding them and by subtracting them 2 x y 2 x − y = 6 − 2 4 x = 4 x = 1 2 x y − 2 x − − y = 6 − − 2 2 y = 8 y = 4 So one vertex is (4, 1) The other two vertices are the x intercepts 2 x 0 = 6 x = 3 One vertex (3, 0) 2 x − 0 = − 2 x = − 1B = −3 Representing the equations graphically we have The point of intersection of the two lines is (6, 1) The solution is (x, y) = (6, 1)
Draw The Graph Of 2x Y 6 And 2x Y 2 0 Shade The Region Bounded By These Lines With X Axis Find The Area Of The Shaded Region Mathematics Topperlearning Com p26nrmm
