Given the function shown in the graph:
f(x).
The function g is a transformation of f.
Let's determine the function which represents g, if g has a y-intercept at -1.
The given function f, from the graph has a y-intercept of:
-5
If g has a y-intercept of -1, it means that the graph of f undergoes a movement upwards to get the function g.
The units of translation will be:
-1 - (-5) = -1 + 5 = 4
This means there was a vertical translation 4 units upwards.
Now, apply the transformation rule for functions.
After a vertical translation 4 units up, the translated function will be:
g(x) = f(x) + 4
Therefore, the function which represents g is:
g(x) = f(x) + 4
ANSWER:
B. g(x) = f(x) + 4