Final answer:
The y-intercept of the function g(x), defined as g(x) = f(x) + 9 where f(x) = -3x - 5, is 4. This is determined by evaluating g(0), resulting in a y-intercept at the point (0, 4).
Step-by-step explanation:
The question asks about finding the y-intercept of the function g(x), which is defined in terms of another function f(x). Given that f(x) is equal to -3x - 5 and g(x) equals f(x) + 9, to find the y-intercept of g(x), we substitute x with 0 in the function f(x) and then add 9. The y-intercept is the point where the function crosses the y-axis, which is when x = 0.
First, we find the value of f(0):
f(0) = -3(0) - 5 = -5
Next, we determine g(0) by adding 9 to the value of f(0):
g(0) = f(0) + 9 = -5 + 9 = 4
Therefore, the y-intercept of g(x) is 4, which means the line representing g(x) crosses the y-axis at the point (0, 4).