Question

Please help don't understand this. The function g is a transformation of f. If g has a y-intercept at -1, which of the following functions could represent g?

Answer 1

Answer: B. g(x) = f(x)+4

Explanation:

The graph shows that f(x) has the y intercept at -5. This is where the red line crosses the vertical y axis. More specifically, the y intercept is located at the point (0,-5)

We're told that g(x) has a y intercept at -1. So we must move f(x) 4 units up to go from y = -5 to y = -1. This is because -5+4 = -1.

Do this for every point on f(x) and you'll end up with g(x) = f(x)+4. Recall that y = f(x). So saying f(x)+4 is the same as y+4 to indicate "shift up 4 units".

f(x) and g(x) have the same slope, but different y intercepts. So they are parallel lines that never cross.