Rational Function Graphs/Word Problems
What is the vertical asymptote of the graph on Ms. E's Screen?
x=-2
Find the horizontal asymptote of the equation f(x)=(12x-2)/(x+2)
y = 12
Solve using cross-multiplication:
x/(2x-3)=3x/(x+11)
3x(2x-3)=x(x+11)
6x^2-9x=x^2+11x
5x^2-20x=0
5x(x-4)=0
x=0, x=4
(v+2)/(v-4)+(7v-42)/(v-4)
(8v-40)/(v-4)
On average how many questions do kids ask per day?
A. 50
B. 100
C. 300
D. 550
C. 300 -- that's about one question every 2.5 minutes
What is the equation of the horizontal asymptote of the graph?
y=-2
Find the vertical asymptote of the function f(x)=(5x-4)/(4x-8)
4x-8=0
4x=8
x=2
Solve for n:
1/n^2+1/n=1/2n^2
n=-1/2
Multiply & Simplify:
[8(r-4)/(r-4)]*9r/(8(r-2))
(write it out on a sheet of paper)
9r/(r-2)
What is the national animal of Scotland?
A. Dragon
B. Unicorn
C. Loch Ness Monster
D. Big Foot
B. Unicorn
The amount of time it takes to finish a construction job depends on how many workers you assign. The time needed can be modeled by the function:
T(x)=(15x+70)/(3x+15)
where x is the number of workers assigned in addition to the boss, and T(x) is the amount of time needed to finish construction, in hours.
What is the vertical asymptote of T(x)?
Find by setting the denominator = 0.
0=3x+15
3x=-15
x=-5
Find the y-intercept of the function:
f(x)=(4x+12)/(x^2+3)
plug in x=0
f(0)=(0+12)/(0+3)=12/3
f(0)=4 or (0,4)
Solve for n:
6-(5/n)=n
multiply both sides by n
6n-5=n^2
0=n^2-6n+5
0=(n-5)(n-1)
n=5, 1
Simplify:
(3x-12)/(3x^2-12x)
Find the GCFs:
3(x-4)/(3x(x-4))
3/(3x)
1/x
Subtract the rational expressions and simplify
5/(12x)-3/4
Multiply 3/4 by (3x/3x) to get common denominator of 12x
5/(12x)-9x/12x=(5-9x)/12x
The amount of time it takes to finish a construction job depends on how many workers you assign. The time needed can be modeled by the function:
T(x)=(15x+70)/(3x+15)
where x is the number of workers assigned in addition to the boss, and T(x) is the amount of time needed to finish construction, in hours.
What is the domain of T(x)?
non-negative integers
(can't have fractional workers and can't have negative workers)
Find the x-intercept(s) of the function:
f(x)=(x^2-4)/(2x+2)
Plug in f(x)=0
0=x^2-4
4=x^2
x=2, -2
Solve for d:
3/(d-1)-8/(d+2)=1
3(d+2)-8(d-1)=1(d-1)(d+2)
3d+6-8d+8=d^2+d-2
0=d^2+6d-16
0=(d+8)(d-2) --> d=-8, d=2
2/(x-6)+7/(x+2)
Multiply to get a common denominator of (x-6)(x+2)
(9x-38)/(x^2-4x-12)
Which of the following is NOT a pet that Ms. E has had?
A. A guinea pig named Fudge
B. A cactus named Richard
C. A goldfish named Freddy
D. A turtle named Zeno
D. A turtle named Zeno