y = log base (x - h) + k
1) Vertical Asymptote: -4
The vertical asymptote is at -4 because when dealing with logs, the vertical asymptote will always be the h value, and since in the original equation you are subtracting it from x, you flip the sign, so instead of positive 4, you get negative 4.
2) Domain: x > -4
When graphing a logarithm, it doesn't cross the vertical asymptote, and it is a positive function, so all of the x values will be greater than -4.
3) X and Y Intercepts: x = -2, y = 1
To find the x-intercept, y has to equal 0, so plug 0 in for y and solve for x. To find the y-intercept, x has to equal 0, so plug in 0 for x and solve for y.
4) Transformations: shifted 4 units to the left, and shifted 1 unit up.
To find the horizontal movement, look at h. If h is positive, then the function has been shifted that many units to the left. If h is negative, then the function has been shifted that many units to the right, To find the vertical movement, look at k. If k is positive, then the function has moved that many units up. If k is negative, then the function has moved that many units down.
