Is this correct?

The function f(x) = x². The graph of g(x) is f(x) translated to the right 3 units and down 3 units. What is the function rule for g(x)?

my awsner

Question

Is this correct?

The function  f(x) = x². The graph of g(x) is f(x) translated to the right 3 units and down 3 units. What is the function rule for g(x)?

my awsner

anonymous · Answer

g(x)=f(x)
g(x)=f(x−3)−3
g(x)=(x−3)−3

anonymous · Answer

@amistre64 
@Agent_Sniffles 
@Helper93

whpalmer4 · Answer

Which one is your answer?

anonymous · Answer

g(x)=(x−3)^2−3

whpalmer4 · Answer

Yes, it's correct, but how could check that if you didn't have me handy? :-)

anonymous · Answer

id be lost:0

whpalmer4 · Answer

No, you wouldn't :-)

Plot a few interesting points on f(x), and plug them into your g(x) and see if they make sense.  For example, f(x) is a parabola with the bottom at (0,0), right?  If we did our translations correctly, g(x) ought to be a parabola with the bottom at (3,-3).  Plug in x = 3 and what do you get for y?  (3-3)^2-3 = 0-3 = -3, so at least one point is in the right spot!  That's probably all we need to check in this case, but if the problem had you do something more complicated, it might be worth doing a few more.  It's easy to see that if we'd made a mistake like writing g(x) = (x+3)^2 -3  that our error would be apparent very quickly when we tried to graph...