Rational Expressions
Rational Functions
Applications of Rational Functions
Radical Expressions, Equations, and Functions
Advanced Literal Equations
100
4/(x-7)div2/(x-7)
2
100
Create a graph, then state the domain and range of the function using interval or inequality notation.
f(x)=1/((1-x)^2)
Domain: (−∞, 1) ∪ (1, ∞)
Range: (0, ∞)
100
Addie, Namanda, and Taylor can paint a room together in 6 hours. If Addie and Namanda could do it in 10 hours, how long would it take Taylor by herself?
15 hours
100
sqrt(8x+4)=6
4
100
What is the y-intercept of the function
g(x)=4x-9sqrt(10x+49)
(0,-63)
200
8/(3x-1)+1/(1-3x)
7/(3x-1)
200
Create a graph, then state the domain and range and any asymptotes or holes for each function.
f(x)=(x-2)/(x-2)
Domain: (−∞, 2) ∪ (2, ∞)
Range: 𝑦 = 1
Holes: (2, 1)
Asymptotes: None
200
To fill a pool, Barb uses two hoses. The first hose is rated to fill the pool in 10 hours. The second hose is rated to fill it in 5 hours. If Barb adds a third hose that uses the slower rate, how long will it take to fill the pool?
2.5 hours
200
sqrt(x-45)=sqrtx-5
49
200
Describe the transformations done on the parent function
f(x)=sqrtx
to create the new function
g(x)=8+sqrt(4x+12)
Vertical shift: up 8
Horizontal shift: left 3
Vertical stretch by factor of: 2
300
(x-10)/(x^2-7x-30)div(5x^2)/(x+3)
1/(5x^2)
300
Create a graph, then state the domain and range and any asymptotes or holes for the function.
f(x)=(x^2+x-6)/(x^2+6x+9)
Domain: (−∞, −3) ∪ (−3, ∞)
Range: (−∞, 1) ∪ (1, ∞)
Holes: None
Asymptotes: HA at 𝑦 = 1 ; VA at 𝑥 = −3
300
Carl and Rick are traveling to a store 5 miles away. Carl is riding a bike, so he’s going 12 mph faster than Rick. If it takes Rick 45 minutes, how long did it take Carl? (hint: compare rates)
~ 0.268 hrs ~ 16.07 minutes
300
sqrt(4x^2-27)=3
+-3
300
Which of the following is the inverse of the function
f(x)=14-2x^2
f^-1(x)=sqrt((14-x)/2)
400
(x-5)/(x^2-x-12)-(3x)/(x-4)
((-3x-1)(x+1))/((x-4)(x+3))
400
Create a graph (you may use a calculator), then state the domain and range and any asymptotes or holes for the function
h(x)=(9x^2-9)/(3x^2+12x+12)
Domain: (−∞, −2) ∪ (−2, ∞)
Range: [−1, ∞)
Holes: None
Asymptotes: HA at 𝑦 = 3 ; VA at 𝑥 = −2
400
A plane flies 450 miles with the wind, and 350 miles against the wind (in the same amount of time). If the wind is blowing at 30 mph, how fast would the plane be going without air helping/hurting?
240 mph
400
sqrt(x^2+6)+sqrt(x^2-3)=3
+-sqrt3
400
Solve for t
A=(t(b+c))/h
t=(Ah)/(b+c)
500
(x-3)/(7x-6)-(x^2)/(14x^2-5x-6)
(x^2-5x-3)/((2x+1)(7x-6))
500
Write a possible function for the graphed function.
f(x)=(x^2-x+1)/(x-1)
(Numerator may vary)
500
C(x)=500/(x+25)
is a function used to calculate the average cost per unit of making 𝑥 units of baseball bats. If the cost per unit is $1.50, how many units have been produced?
About 308 units of baseball bats
500
sqrt(x^2+8)-sqrt(x^2-4)=2
sqrt8
500
Solve for m:
T=2pisqrt(m/k)
m=k(T/(2pi))^2