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- (4) Decide which of the following maps f: R2 R2 are answers. isometries. Justify your (iv.) f(x, y) = (2x+3y,+2);(4) Decide which of the following maps f R2 R2 are isometries. Justify your answers. : (v.) f(x,y) = (1-x, 3+ y).What is the image of a horizontal line y = k € R under the mapping W z²? =
- 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 =2) The contour map of f(x, y) is shown below. Use it to find fx (1,3) 10 10 8 8 6 =2 6 0 x=2 6 8 10Determine whether each of the following maps from R? to R³ is linear. Prove your answers. (a) F((x,y)) = (x², y², x + y) (b) G( (x, y)) = (x+ y, 2x, 3y) (c) H((x, y)) = (x+1,y +2,0)
- 2. Let f a function such that f (-2) = 6, f (0) = – 3, ƒ (3) = 0. Give the coordinates of three points on the graph of y = f(x + 4).6) The contour map of a function C(x, y) is shown below. Use it to answer the following questions. -6 37 -2/ 2 O i O P -2 0 -2- -1 3 d S J a. Estimate the value of C(-1,4). (Your answer does not need to be exact.) b. Is Cx (-4,2) positive, negative, or zero? c. In which direction is VC at the point (0,5)? d. C has a critical point the point labelled P, near (-1.3,0). Is this point a local minimum, local maximum, or saddle point?3. Provide a small table and contour maps for the following functions. You need not attempt a three dimensional representation. Be sure to indicate regions of the plane that fall outside the domain of the function. (a) f(x,y) = x - y D (b) f(x, y) = 2/ (c) f(x,y)=√16 - x² - y²
- 5. Given f(x) = -2/4x – 8 + 1 а. Determine the parent function b. Determine the mapping rule c. Map the points to their new coordinates (6) (x, y) d)Graph both the parent function and the new function after transformations on the Cartesian plane provided: 10 5 -5 10 15 20 25 30 -5 -10The points in the left column are on the graph of y = f(x), Match the point on the left to the point where it is located if each point is shifted left 4 units and up 2 units. O Hold and drag to reorder (0, – 3) = (-5, – 2) (1, – 4) -4, – 1) (-1,0) = (0,3) (4,5) -3, – 2) = (-3,2) = (-5,2) = (0,7) = (-4,1) SubmitIn the xy-plane, line k intersects the y-axis at the point (0, –6) and passes through the point (2, 2). If the point (20, w) lies on line k, what is the value of w ?
