(4) Decide which of the following maps f R2 R2 are isometries. Justify your answers. : (v.) f(x,y) = (1-x, 3+ y).

(4) Decide which of the following maps ƒ R2 R² answers. (i.) f(x,y)=(y, x); -> are isometries. Justify your

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:

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 =

Determine 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)

The 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)

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 10

Let A = {4, 5, 7} and B = {x, y}. Let p1 and p2 be the projections of A ✕ B onto the first and second coordinates. That is, for each pair (a, b)  A ✕ B, p1(a, b) = a and p2(a, b) = b. (a) Find p1(4, y) and p1(7, x) What is the range of p1? (Enter your answer in set-roster notation.) (b) Find p2(4, y) and p2(7, x). What is the range of p2? (Enter your answer in set-roster notation.)

Let A = {4, 5, 7} and B = {x, y}. Let p1 and p2 be the projections of A ✕ B onto the first and second coordinates. That is, for each pair (a, b)  A ✕ B, p1(a, b) = a and p2(a, b) = b. (a) Find p1(4, y) and p1(7, x). What is the range of p1? (Enter your answer in set-roster notation.) (b) Find p2(4, y) and p2(7, x). What is the range of p2? (Enter your answer in set-roster notation.)

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 y