Each statement describes a transformation of the graph of f(x) = 3x. Which statement correctly describes the graph of g(x) = 3(x - 5) + 4?

A.

The graph of g(x) is the graph of f(x) translated up 4 units and left 5 units.

B.

The graph of g(x) is the graph of f(x) translated down 5 units and left 4 units.

C.

The graph of g(x) is the graph of f(x) translated down 5 units and right 4 units.

D.

The graph of g(x) is the graph of f(x) translated up 4 units and right 5 units.

The population of a small town, P, as a function of time, t, in years past 1940 is given below.

P = 3,236 + 275t

For which of the following years was the population of the town 9,836?
A.
1974
B.
1934
C.
1964
D.
1924

In g(x) we are subtracting 5 from x and because it's being done to x it means the shift is horizontal (just like the x-axis is horizontal). To figure out which way the graph shifts make that expression equal to zero and solve:

x-5 = 0

x=5 ----> positive 5 so this means 5 units to the right.

The +4 is being added to the entire function and this means it moves up 4 because it's positive 4.