QueenNerdy889
04.08.2019 •
Mathematics
Hello, can someone explain on how to do this? you! graph the logarithmic function. y=log(x-3)
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Ответ:
We are given a log function.
y= log(x-3).
Note: A log never takes 0 or negative values.
We have x-3 there.
The value of x-3 should be greater than 0.
Let us solve it for x.
x-3>0.
Adding 3 on both sides, we get
x-3+3 >0+3.
x>3.
So, we got domain of the given function x>3. So, we can take any value greater than 3 for x.
Let us make a table of different values of x and y for the given function
______________________________________
x y=log(x-3)
______________________________________
4 y=log(4-3) = log(1) = 0
5 y=log(5-3) = log(2) = 0.3010
6 y=log(6-3) = log(3) = 0.4771
7 y=log(7-3) = log(4) = 0.6021
10 y=log(10-3)= log(7) = 0.8450
______________________________________
Ploting points on the graph.
Ответ:
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.
Ответ: