Answer:
g(x) = f(x) - 3
k = 3
Explanation:
A linear function is in the form f(x) = mx + b, where m is the slope and b is the y intercept (value of y when x = 0).
Translation is the movement of a function either up, down, left or right.
If a function y = f(x) is translated k units up, the new function produce would be y = f(x) + k.
If a function y = f(x) is translated k units down, the new function produce would be y = f(x) - k.
If a function y = f(x) is translated k units left, the new function produce would be y = f(x-k).
If a function y = f(x) is translated k units right, the new function produce would be y = f(x + k).
From the image attached, we can see that the graph of g(x) is below that of f(x), hence f(x) was translated k units down to form g(x), hence:
g(x) = f(x) - k
To find the value of k, we see that the y intercept of f(x) is 1 and the y intercept of g(x) = -2, hence k = 1 - (-2) = 3
F(x) was translated 3 units down to form g(x), hence:
g(x) = f(x) - 3