Steps:
1) determine the domain
2) determine the extreme limits of the function
3) determine critical points (where the derivative is zero)
4) determine the intercepts with the axis
5) do a table
6) put the data on a system of coordinates
7) graph: join the points with the best smooth curve
Solution:
1) domain
The logarithmic function is defined for positive real numbers, then you need to state x - 3 > 0
=> x > 3 <-------- domain
2) extreme limits of the function
Limit log (x - 3) when x → ∞ = ∞
Limit log (x - 3) when x → 3+ = - ∞ => the line x = 3 is a vertical asymptote
3) critical points
dy / dx = 0 => 1 / x - 3 which is never true, so there are not critical points (not relative maxima or minima)
4) determine the intercepts with the axis
x-intercept: y = 0 => log (x - 3) = 0 => x - 3 = 1 => x = 4
y-intercept: The function never intercepts the y-axis because x cannot not be 0.
5) do a table
x y = log (x - 3)
limit x → 3+ - ∞
3.000000001 log (3.000000001 -3) = -9
3.0001 log (3.0001 - 3) = - 4
3.1 log (3.1 - 3) = - 1
4 log (4 - 3) = 0
13 log (13 - 3) = 1
103 log (103 - 3) = 10
lim x → ∞ ∞
Now, with all that information you can graph the function: put the data on the coordinate system and join the points with a smooth curve.
Answer:
y=66(.25)x
(obviously the x is supposed to be an exponent but idk how to make it an exponent)
Step-by-step explanation:
Answer:
On Wednesday
Step-by-step explanation:
In this question, We have Alana practicing for three days. We now need to know in which of the days has she practiced closest to 2 hours. Hence, what we are to do here is simply find which of the practicing hours is nearest to 2hours.
The best thing to do here is to work with minutes. Hence whatsoever fraction we are having would be worked with based on minutes. Let’s do this!
On Monday, she practiced 11/4 hours. This means she practiced 11/4 * 60 minutes = 165 minutes
On Tuesday, practice was for 19/8 hours. This means she had practiced for 19/8 *60 = 142.5 minutes
Lastly, on Wednesday, her practice time was 2.6 hours and that is 2.6 * 60 = 156 minutes
Kindly note that 2 hours is same as 120 minutes. We just need to know which of these minutes is closest to 120 minutes. From what we have, 142.5 is the closest.
This means that her practice on Wednesday is the closest to two hours.
