1. state the domain of the rational function. (2 points)
f(x) = thirteen divided by quantity ten minus x.

a) all real numbers except -10 and 10
b) all real numbers except 13
c) all real numbers except 10
d) all real numbers except -13 and 13

2. state the vertical asymptote of the rational function. (2 points)
f(x) = quantity x minus six times quantity x plus six divided by quantity x squared minus nine.

a) x = 6, x = -6
b) x = 3, x = -3
c) x = -6, x = 6
d) none

3. state the horizontal asymptote of the rational function. (2 points)
f(x) = quantity x squared plus four x minus seven divided by quantity x minus seven.

a) none
b) y = -4
c) y = 7
d) y = 6

4. state the horizontal asymptote of the rational function. (2 points)
f(x) = quantity x squared plus eight x minus two divided by quantity x minus two.

a) none
b) y = 1
c) y = -8
d) y = 2

5. give an example of a rational function that has a horizontal asymptote at y = 0 and a vertical asymptote at
x = 2 and x = 1.

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.  

step-by-step explanation:

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