A graph shows f(x) = 0.5x – 1. • Graph and write the equation for g(x) by translating f(x) up 2 units and then stretching it vertically by the factor 2. • Graph and write the equation for h(x) by stretching f(x) vertically by the factor 2 and then translating it up 2 units. • Compare the graphs of g(x) and h(x).

Answer:g(x) = x + 2h(x) = xh(x) is the parent function of g(x)Step-by-step explanation:* Lets explain how to solve the problem- If the function f(x) translated vertically up 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.  * Lets solve the problem- The graph of f(x) is attached- f(x) = 0.5x - 1- f(x) translated 2 units up ∴ We will add f(x) by 2 units ∴ The new function is f(x) + 2- Then f(x) is stretched vertically by the factor 2∴ We will multiply f(x) after translated up by 2∴ g(x) = 2[f(x) + 2]∴ g(x) = 2[0.5x - 1 + 2] = 2[0.5x + 1] = x + 2∴ g(x) = x + 2- The graph of g(x) is attached- f(x) = 0.5x - 1- f(x) is stretched vertically by the factor 2∴ We will multiply f(x) by 2- Then f(x) translated 2 units up ∴ We will add f(x) after stretching by 2 units ∴ h(x) = 2[f(x)] + 2∴ h(x) = 2[0.5x - 1] + 2 = x - 2 + 2 = x∴ h(x) = x- The graph of h(x) is attached∵ h(x) = x∵ g(x) = x + 2∴ h(x) is the parent function of g(x)- If we translate h(x) 2 units to the left, then its image is g(x)- If we translate h(x) 2 units up, then its image is g(x)