Part A: k * f(x)
In this case, the value of k affects the functions in that the y-intercept changes, that is, the value of k determines the y-intercept of the function. For example, when we have a k = 3, the y-intercept for the function is 3, if k = 5, the y-intercept is 5, and so on.
Part B: f(x + k)
In this case, we have a shift in the x-axis. The function is shifted k units to the left respecting the original function. For example, if k = 1, the function is shifted one unit to the left, and so on.
Part C: f(x) + k
In this case, we have a shift in the y-axis. The function is shifted k units in the y-axis.
For example, if we have that k = 1, the function is shifted one unit upward in the y-axis.
If the value is k = 2, the function is shifted two units upward in the y-axis, and so on.