The graph of g(x) was translating the graph of f(x) down 2 units.

Question

This graph will go through the points of just below -1 on the y-axis and just past the right tfo the zero on the x-axis. I can't figure out what the equation is. I know the answer is f(x)=3x+1 but I don't understand how to get that answer. 

Answer 1

I'm not sure exactly what you're asking...

 

If f(x)=3x+1 was translated down 2 units to create g(x), then:

g(x) = f(x) - 2 = (3x + 1) - 2 = 3x - 1

So g(x) = 3x - 1

 

If g(x) was translated down 2 units to create f(x)=3x+1, then

g(x) - 2 = f(x)

g(x) = f(x) + 2 = (3x+1) + 2 = 3x +3

so g(x) = 3x + 3

Answer 2

I think of it this way:

f(x) simply means "a function of x" = f(x) changes with changes in x.  When we graph, usually f(x) = y, the vertical graph axis.  So your problem is now y=3x+1

So input several values for x;  try 0 (zero), +1, and -1:

y = 3(0) + 1 = 1.  Plot that point on the X/Y graph as (0,1) (means x=0, y=1)

y = 3(+1) +1 = 4.  Plot that as (1,4)  (means x=1, y=4)

y = 3(-1) +1 = -2.  Plot that as (-1,-2)  (means x=-1, y=-2)

You should see a straight line from upper right to lower left, passing the x/y axis (at 0,0) just to the left of x=0.  Exactly where?  Set y=0 and solve for x:

0 = 3x + 1

3x = -1

x = - 1/3   (means line passes through the point (-1/3, 0) (means when y=0, x= -1/3)