Answer:
Step-by-step explanation:
Given
Required
Determine 
The implication of the question is to solve for
Given that
and
would be
Collect Like Terms
Open Bracket
Collect Like Terms
1)
The domain
is every value of x for which f(x) is a real number.
f(x) = 13 / (10-x)
The only x value that would not produce a real number for f(x) is 10, since you
cannot divide a number by zero. Answer is C
2)
F(x)
=(x-6)(x+6)/(x2 - 9)
The vertical asymptotes are x=3 and x=-3. Graph the function on a graphing
calculator to observe the behavior of the function at these points. There is
both a positive and negative vertical asymptote a both x=3 and x=-3. Keep in
mind that the denominator approaches zero at these points, and thus f(x) approaches
either positive or negative infinite, depending on whether the denominator, however small, is a positive or
negative number. Answer is B) 3, -3
3)
F(x) = (x2
+ 4x-7) / (x-7)
Although there is a vertical asymptote as x=7, there is no horizontal asymptote.
This makes sense. As X gets bigger, there is nothing to hold y back from
getting greater and greater. X2 is the dominant term, and it’s only
in the numerator. A) none
4)
(x2 +
8x -2) / (x-2)
This function is very similar in structure to the previous one. Same rules
apply. Dominant term only in the numerator means no horizontal asymptote.
A)None
5)
Our
function approaches 0 as x approaches infinite, and has a vertical asymptote at
x=2 and x=1.
Here’s an easy example: 10 / ((x-2)*(x-1)). At x=2 and x=1, there is both a
positive and negative vertical asymptote. As x approaches infinite, the
numerator is dominated by the denominator, which contains x (actually x2 ),
and thus y approaches zero.
Answer:
48 miles multiplied by x amount of gallons
Step-by-step explanation:
