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).

g(x) = x + 2

h(x) = x

h(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)