Answer:
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)
