Answer:
[tex](0, log_{b}(-k)), k < 0[/tex]
Step-by-step explanation:
[tex]y = \log_{b}(a - k)[/tex]
To find the y-intercept, set a = 0 and solve for y.
[tex]y = \log_{b}(0 - k)\\y = \log_{b}(-k)[/tex]
This equation is undefined for k ≥ 0.
There is a y-intercept only if k < 0. Only then can the argument of the log function be positive.
The y-intercept is at
[tex]\mathbf{(0, log_{b}(-k)), k < 0}[/tex]
For example, if b = 2 and k = -3, log₂(3) = 1.585
The intercept is at (0, 1.585).
