00:02
We can only evaluate logarithms that are greater than 0.
00:11
So x plus 5 has to be greater than 0.
00:17
And so that would mean x has to be greater than negative 5.
00:20
So the domain would be from negative 5 not included to infinity.
00:26
The range is going to be all reals.
00:32
The vertical asymptotes, since this is going normally, it's the y -axis.
00:37
This is going to be moved to the left five.
00:41
So the vertical asymptote will be x equals negative five.
00:50
For part d, write this down here, the exact value of the y -intercept is when x is zero.
00:59
So that would be y equals negative three plus log base two of five.
01:11
Would be what i would say is the exact value because when you plug in zero for x you're going to have a log base to a 5 the exact value of the x intercept well that's when the function is equal to 0 and so we need to solve for x here add 3 to both sides then do exponential base 2 to both sides to get rid of log base 2 2 to the 3 is 8 subtract 5 to both sides and x equals 3 is your x intercept.
01:57
I'm going to take note of that...