Answer:
Look to the attached graph
Step-by-step explanation:
* Lets explain the difference between the graphs of f(x) and g(x)
∵ f(x) = IxI
∵ g(x) = IxI - 4
- If we add are subtract f(x) by k, where k is a constant that means
we translate f(x) vertically
- If g(x) = f(x) + k
∴ f(x) translated vertically k units up
- If g(x) = f(x) - k
∴ f(x) translated vertically k units down
∵ g(x) = IxI - 4
∵ f(x) = IxI
∴ g(x) = f(x) - 4
∴ f(x) translated vertically 4 units down
∴ The graph of f(x) will translate down 4 units
∵ The origin point (0 , 0) lies on f(x)
∴ The origin point (0 , 0) will translate down by 4 units
∴ Its image will be point (0 , -4)
∴ Point (0 , -4) lies on the graph of g(x)
- So you can translate each point on the graph of f(x) 4 units down to
graph g(x)
# Two point on the left part
∵ Point (-2 , 2) lies on f(x)
∴ Its image after translation 4 units down will be (-2 , -2)
∴ Point (-2 , 2) lies on g(x)
∵ Point (-7 , 7) lies on f(x)
∴ Its image after translation 4 units down will be (-7 , 3)
∴ Point (-7 , 3) lies on g(x)
# Two point on the right part
∵ Point (3 , 3) lies on f(x)
∴ Its image after translation 4 units down will be (3 , -1)
∴ Point (3 , -1) lies on g(x)
∵ Point (8 , 8) lies on f(x)
∴ Its image after translation 4 units down will be (8 , 4)
∴ Point (8 , 4) lies on g(x)
* Now you can draw the graph with these 5 points
