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- Let G(u, v) = (2u + v, 5u + 11v) be a map from the uv-plane to the xy-plane. Find the image of the line v = 4u under G in slope-intercept form. (Use symbolic notation and fractions where needed.) y =Let G(u, v) = (5u + v, 30u + 13v) be a map from the uv-plane to the xy-plane. Find the image of the line through the points (u, v) = (1, 1) and (u, v) = (1,–1) under G in slope-intercept form. (Express numbers in exact form. Use symbolic notation and fractions where needed.) equation:Determine a mapping of the form (x, y)) from y = f(x) for each of the following. y = 3f(2x) y=-11 7x y=-2r(-3x)
- Sketch the graph of f(x,y) = 5x + 4y – 20. State the domain and range of the function. Which of the following surface graphs represents f(x,y) = 5x+ 4y - 20? OA. OB. OC. (0,0,20) (0,0,20) 5,0,0) (4,0,0) 0,-4,0) (0,-5,0) (0,5,0) (-4,0,0) K(0,0.-20) y ySketch a contour map and graph of. a. g(x,y) = 9x2 +4y2 b. z = y/xThe function f(x) has been transformed to y = -2f(-x+3)+1, which has resulted in the mapping of (4, -2) to Select one: O a. (-5,5) O b. (-1,5) O c. (-7,5) O d. (11, -3)
- Determine a mapping of the form (x, y) → (, ) for the inverse of a relation. a. (x, f(x)) b. (x, y¹) c. (y, f(x)) d. (y, x)(2) The figure below shows the contour diagram of g(x, y). a) Mark the points on the contours where b) Mark the points on the contours where Iz = 0. Iy = 0. 2 2 1 1 -1 -1 -2 -2 -1 0 -2 -2 -1 0 1 2 1 2Use the Jacobian of a coordinate transformation to find the area of the parallelogram bounded by the lines y = 3x, y = 3x+2, y = 1−x, y = 4−x.
- Describe (in the form y = f(x)) the images of the lines u = 6 and v = 6 under the mapping G(u, v) = (,u? – v). (Express numbers in exact form. Use symbolic notation and fractions where needed.) image of u = 6: y = image of v = 6: y =Find the Cartesian equation of the image of the line y = 2 under the mapping z → z 2Sketch the image. If the pre-image point move on y = 2 from left to right, what is the orientation of the image point?Find the equation of locus of a point P such that the distance of P from the origin is twice the distance of P from A (1,2).
