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:
Step-by-step explanation:
If you want to factor
, you could throw that into the quadratic formula with a = 1, b = 11 and c = 0, but the easier thing to do is to factor out what's common in those 2 terms. m is common, so when we factor it out:
That's the factored form.
By the Zero Product Property, either
m = 0 or m + 11 = 0.
So the 2 solutions to this are
m = 0 or m = -11
Not sure how far you need to go with this.
Answer:
x = y = 2√2
Step-by-step explanation:
Find the diagram attached
To get the unknown side x and y, we need to use the SOH CAH TOA identity
Opposite side = x
Adjacent = y
Hypotenuse = 4
Sin theta = opposite/hypotenuse
sin 45 = x/4
x = 4 sin 45
x = 4 * 1/√2
x = 4 * 1/√2 * √2/√2
x = 4 * √2/√4
x = 4 * √2/2
x = 2√2
Similarly;
cos theta = adjacent/hypotenuse
cos 45 = y/4
y = 4cos45
y = 4 * 1/√2
y = 4 * 1/√2 * √2/√2
y = 4 * √2/√4
y = 4 * √2/2
y = 2√2
Answer:
Option A
y=-4/3x+7
Step-by-step explanation:
To solve this, we need to understand the various components of the equation of a straight line.
A straight line has the equation: y =mx + c
<em>m</em> is the slope and<em> c</em> is the intercept on the y-axis. If we can get these two components, we can figure out the equation for the new line.
Calculating the slope, <em>m</em>
To obtain the slope of the new line, we use the fact that it is perpendicular to the slope of the line y = 3/4x-2.
This means that
3/4 X <em>m</em> = -1
<em>m</em> = -4/3
To obtain the intercept, <em>c</em>
The intercept can be obtained by adding 3 to the y-component of (0, 4).
This will give (0, 7). Hence the intercept c will be 7.
Therefore, the equation of the line will be y = -4/3x+7. Option A
