Answer:
Vertical asymptote: 
Horizontal asymptote: 
or x axis.
Step-by-step explanation:
The rational function is given as:
Vertical asymptotes are those values of 
for which the function is undefined or the graph moves towards infinity.
For a rational function, the vertical asymptotes can be determined by equating the denominator equal to zero and finding the values of .
Here, the denominator is 
Setting the denominator equal to zero, we get
Therefore, the vertical asymptote occur at 
.
Horizontal asymptotes are the horizontal lines when tends towards infinity.
For a rational function, if the degree of numerator is less than that of the denominator, then the horizontal asymptote is given as 
.
Here, there is no term in the numerator. So, degree is 0. The degree of the denominator is 3. So, the degree of numerator is less than that of denominator.
Therefore, the horizontal asymptote is at or x axis.
Answer:
3 h(x) = 4 sin(2x + π) + 3
Step-by-step explanation:
Supposing 2x-7 were a factor, then 7/2 would be a root. Use synth. div. to determine whether 7/2 actually is a root:
__________________________
7/2 / 6 -21 -4 24 -35
21 0 -14 35
----------------------------------------
6 0 -4 10 0
Since the remainder is zero, 7/2 is a root and 2x - 7 is a factor.
You could check out the other possible factors in the same manner.
Answer:
B. 16 hrs
Step-by-step explanation:
Distance = rate × time
The best way to do this is to make a table with the info. We are concerned with the trip There and the Return trip. Set it up accordingly:
d = r × t
There
Return
The train made a trip from A to B and then back to A again, so the distances are both the same. We don't know what the distance is, but it doesn't matter. Just go with it for now. It'll be important later.
d = r × t
There d
Return d
We are also told the rates. There is 70 km/hr and return is 80 km/hr
d = r × t
There d = 70
Return d = 80
All that's left is the time column now. We don't know how long it took to get there or back, but if it took 2 hours longer to get There than on the Return, the Return trip took t and the There trip took t + 2:
d = r × t
There d = 70 × t+2
Return d = 80 × t
The distances, remember, are the same for both trips, so that means that by the transitive property of equality, their equations can be set equal to each other:
70(t + 2) = 80t
70t + 140 = 80t
140 = 10t
14 = t
That t represents the Return trip's time. Add 2 hours to it since the There trip's time is t+2. So 14 + 2 = 16.
B. 16 hours
