Title: Chapter 12 Rational Equations and Functions
Course: quiz duplicate error

Q: Graph the function.

f(x) = [Image]
- [Image]
- [Image]
- [Image]
- [Image]
A: [Image]

Q: Describe the graph of the function.

y = [Image]
- The graph is an absolute value function with vertex (7, –4).
- The graph is an absolute value function with vertex (–4, –7).
- The graph is an absolute value function with vertex (–4, 7).
- The graph is an absolute value function with vertex (4, –7).
A: The graph is an absolute value function with vertex (4, –7).

Q: Describe the graph of the function.

y = 4x^2 + 16x – 18
- The graph is a parabola with axis of symmetry at x = 2.
- The graph is a parabola with axis of symmetry at x = 18.
- The graph is a parabola with axis of symmetry at x = 4.
- The graph is a parabola with axis of symmetry at x = –2.
A: The graph is a parabola with axis of symmetry at x = –2.

Q: Simplify the rational expression.

[Image]
- [Image]
- [Image]
- [Image]
- [Image]
A: [Image]

Q: Describe how the graph of g(x) = [Image] + 5 is a translation of g(x) = [Image].
- It is a translation of g(x) = [Image], 4 units right and 5 units down.
- It is a translation of g(x) = [Image], 4 units right and 5 units up.
- It is a translation of g(x) = [Image], 4 units left and 5 units up.
- It is a translation of g(x) = [Image], 4 units left and 5 units down.
A: It is a translation of g(x) = [Image], 4 units right and 5 units up.

Q: Graph the function.

f(x) = [Image] + 1
- [Image]
- [Image]
- [Image]
- [Image]
A: [Image]

Q: What value of x makes the denominator of the function equal zero?
y = [Image]
- 12
- 0.08
- –0.08
- –12
A: –12

Q: Graph the function.

y = [Image]
- [Image]
- [Image]
- [Image]
- [Image]
A: [Image]

Q: The graph of the function y = [Image] is shown on the left below. The graph on the right is the same graph translated right three units and up three units. What is the equation of the graph on the right.
[Image] [Image]
- y = [Image] – 3
- y = [Image] + 3
- y = [Image] + 3
- y = [Image] – 3
A: y = [Image] + 3

Q: Simplify the rational expression.

[Image]
- [Image]
- –1
- [Image]
- [Image]
A: [Image]

Q: Identify the asymptotes of the graph.
[Image]
- x = –2, y = –1
- x = 2, y = 1
- x = 1, y = –2
- x = –1, y = 2
A: x = 2, y = 1

Q: Describe the graph of the function.

y = [Image]
- The graph is the radical function y = [Image] shifted right 6 units and up 2 units.
- The graph is the radical function y = [Image] shifted left 6 units and up 2 units.
- The graph is the radical function y = [Image] shifted right 6 units and down 2 units.
- The graph is the radical function y = [Image] shifted left 2 units and up 6 units.
A: The graph is the radical function y = [Image] shifted right 6 units and up 2 units.

Q: Multiply.

[Image]
- [Image]
- [Image]
- [Image]
- [Image]
A: [Image]

Q: Add or subtract.

[Image]
- [Image]
- [Image]
- [Image]
- [Image]
A: [Image]

Q: Divide.

[Image]
- [Image]
- [Image]
- [Image]
- [Image]
A: [Image]

Q: The rate of discount, R, can be determined using the formula [Image], where P is the regular price of an item and D is the discount, or amount saved off the regular price. Find the rate of discount on a sweater with a regular price of $39 that is on sale for $27. If necessary, round to the nearest hundredth.
- 1.69
- 1.31
- 0.31
- 0.69
A: 0.69

Q: A rectangle has an area of x^3 + x^2 – 7x + 2 square meters and a width of x – 2 meters. Find its length.
- x^2 + 2x – 3 meters
- x^2 + x – 7 meters
- x^2 + 3x – 1 meters
- x^2 – 3x + 5 meters
A: x^2 + 3x – 1 meters

Q: Find the reciprocal of the expression.
[Image]
- [Image]
- [Image]
- [Image]
- [Image]
A: [Image]

Q: A board of length [Image] m was cut into two pieces. If one piece is [Image] m, express the length of the other board as a rational expression.
- [Image]
- [Image]
- [Image]
- [Image]
A: [Image]

Q: Katalin drove 180 miles on her vacation. She drove an average of 1.5 times faster on the second 90 miles of her trip than she did on the first 90 miles of her trip. Which expression represents the time she spent driving. Let x = her speed on the first half of the trip.
- [Image]
- [Image]
- 150x
- [Image]
A: [Image]

Q: Find the LCD of the pair of expressions.
[Image]
- 18x^6y^3
- 6x^6y^3
- 6x^7y^4
- 18x^7y^4
A: 6x^7y^4

Q: Simplify the rational expression.

[Image]
- x^2 – 5
- x + 5
- –x – 5
- [Image]
A: –x – 5

Graph the following function.
[Image]
[Image]

James, Kelly, Hector, and Kyla are painting a house. James could paint the house in 9 hours, Kelly could paint it in 7 hours, Hector could paint it in 6 hours, and Kyla could paint it in 10 hours. How long will it take them to paint it together?

At a pizza parlor, Jerome has a choice of pizza toppings and sizes. The topping choices are sausage, onions, and pineapple. The size choices are mini and small. Draw a tree diagram that shows the number of possible pizza combinations that Jerome can order.

Q: Solve the equation. Check your solution.

[Image]
- x = [Image]
- x = [Image]
- x = [Image]
- x = [Image]
A: x = [Image]

Q: 3 bananas are to be selected from a group of 9. In how many ways can this be done?
- 1
- 362,880
- 504
- 84
A: 84

Simplify the following expression. Show your work.
[Image]

Explain how to determine when combinations should be used and when permutations should be used.

Q: Simplify the expression.

[Image]
- 24
- 720
- 30
- 36
A: 24

Explain the steps used to divide a polynomial by a polynomial.

Q: Suppose Ruth Ann has 3 routes she can choose from to get from school to the library, and 5 routes from the library to her home. How many routes are there from Ruth Ann’s school to her home with a stop at the library?
- 9
- 60
- 15
- 25
A: 15

Q: Prestige Builders has a development of new homes. There are four different floor plans, seven exterior colors, and an option of either a two-car or a three-car garage. How many choices are there for one home?
- 34
- 96
- 64
- 56
A: 56

Q: Each of four friends orders a sweatshirt from a catalog. There are 14 colors of sweatshirts, 7 of which are all cotton and 7 of which are a blend. Each one orders a different color (no repeats) at random. What is the probability that the friends order only cotton sweatshirts?
- [Image]
- [Image]
- [Image]
- [Image]
A: [Image]

Q: Simplify the expression.

[Image]
- 2
- 1,814,400
- 3,628,800
- 80
A: 1,814,400

Write and simplify the rational expression that represents the probability of randomly hitting the unshaded region of the rectangle. Show all of your work.
[Image]

Q: You and six friends play a game where each person writes down his or her name on a scrap of paper, and the names are randomly distributed back to each person. Find the probability that everyone gets back his or her own name.
- 5,040
- 720
- [Image]
- [Image]
A: [Image]

Q: A group of college students is volunteering for Homes for the Community during their spring break. They are putting the finishing touches on a house they built. Working alone, Wade can paint a certain room in 7 hours. Rhonda can paint the same room in 5 hours. How long will it take them working together to paint the room? Round your answer to the nearest hundredth if necessary.
- 17.5 hours
- 0.08 hours
- 6 hours
- 2.92 hours
A: 2.92 hours

Q: Solve the equation. Check your solution.

[Image]
- x = 6
- x = 5
- x = 5 or –2
- x = 6 or –1
A: x = 6 or –1

Q: Simplify the expression.

[Image]
- 12
- 24
- 4
- 2
A: 12

Q: A yogurt shop offers 6 different flavors of frozen yogurt and 12 different toppings. How many choices are possible for a single serving of frozen yogurt with one topping?
- 144
- 72
- 36
- 665,280
A: 72

Q: How many different arrangements can be made with the letters in the word POWER?
- 120
- 20
- 25
- 100
A: 120

Q: Solve the equation. Check your solution.

[Image]
- x = [Image]
- x = 2
- x = [Image]
- no solution
A: x = [Image]

Q: Solve the equation. Check your solution.

[Image]
- x = 1, –2
- x = –2
- x = –2, 0
- x = 0
A: x = –2

Q: You own 6 hats and are taking 4 on vacation. In how many ways can you choose 4 hats from the 6?
- 360
- 720
- 1
- 15
A: 15

Q: You and two friends visit a pizza shop. There are 14 toppings. 6 toppings are meat and the rest are vegetable. Each of you orders a different topping (no repeats) at random. What is the probability that your group orders only meat toppings?
- [Image]
- [Image]
- [Image]
- [Image]
A: [Image]

Q: Solve the equation. Check your solution.

[Image]
- no solution
- x = 2
- x = –4
- x = –2
A: x = –2

Q: Solve the equation. Check your solution.

[Image]
- x = 8
- x = [Image]
- x = 4
- no solution
A: x = 8

Q: Jessica cannot remember the correct order of the five digits in her ID number. She does remember that the ID number contains the digits 9, 0, 3, 1, 5. What is the probability that the first four digits of Jessica’s ID number will all be odd numbers?
- [Image]
- [Image]
- [Image]
- [Image]
A: [Image]

Q: [Image]
- 35
- 210
- 5,040
- 1
A: 35

Simplify.
[Image]

Q: 9 students volunteer for a committee. How many different 7-person committees can be chosen?
- 181,440
- 362,880
- 1
- 36
A: 36

Q: In how many ways can 12 basketball players be listed in a program?
- 479,001,600
- 1
- 665,280
- 12
A: 479,001,600