Write a function g whose graph represents the indicated transformation of the graph of f(x)=-2|x-4|+2​

Answer:g(x) = -Ix - 4I + 1Step-by-step explanation:* Lets revise some transformation- If the function f(x) translated horizontally to the right by h units, then  the new function g(x) = f(x - h) - If the function f(x) translated horizontally to the left by h units, then  the new function g(x) = f(x + h) - If the function f(x) translated vertically up by k units, then the new  function g(x) = f(x) + k - If the function f(x) translated vertically down by k units, then the  new function g(x) = f(x) – k - A vertical stretching is the stretching of the graph away from the  x-axis - If k > 1, the graph of y = k • f(x) is the graph of f(x) vertically  stretched by multiplying each of its y-coordinates by k. - A vertical compression is the squeezing of the graph toward  the x-axis. - If 0 < k < 1 (a fraction), the graph of y = k • f(x) is the graph of f(x)  vertically compressed by multiplying each of its y-coordinates by k. - If k should be negative, the vertical stretch or compress is followed  by a reflection across the x-axis.   * Lets solve the problem∵ The graph of f(x) represented by the function f(x) = -2Ix - 4I + 2∵ The y-intercept of f(x) is -6 and y-intercept of g(x) is -3∵ -3/-6 = 1/2∴ We will multiply f(x) by 1/2 to get the y-intercept of g(x)- That means f(x) is compressed vertically by scale factor 1/2 to be g(x)∴ g(x) = 1/2 [ -2Ix - 4I + 2]∴ g(x) = -Ix - 4I + 1- To be sure from the answer check the point (4 , 2) in f(x), when   we multiply the y-coordinate by 1/2 the point change to (4 , 1)   which is belong to g(x) that means f(x) translate 1 unit down to be   g(x)∴ g(x) = -Ix - 4I + 1