Algebra II - CH 4 Test

Question 1

can you cancel matching parts in addition/subtraction of a rational expression?

Answer 1

no
5x-10/5x does not equal -10

Question 2

how do you multiply rational functions?
(3 steps)

Answer 2

1. factor numerator and denominator
2. cancel out common factors
3. multiply straight across

Question 3

how do you divide rational functions?
(2 steps)

Answer 3

1. keep, change, flip
2. follow multiplication steps

Question 4

how do you simplify rational functions?
(2 steps)

Answer 4

1. factor numerator and denominator
2. cancel out common factors

Question 5

how do you add/subtract rational functions?
(3 steps)

Answer 5

1. factor the denominators (if possible)
2. common denominator (denominator times denominator)
3. add/subtract the numerator

Question 6

how do you solve complex fractions?
(method 1, 4 steps)

Answer 6

1. create a single fraction in the numerator
2. create a single fraction in the denominator
3. divide (keep, change, flip, multiply)
4. simplify

Question 7

how do you solve rational equations?
(method 1/method 2)

Answer 7

method 1: multiply each side by the LCD
method 2: cross multiplication

Question 8

what is an extraneous solution?

Answer 8

a proposed solution that does not make sense and is not a solution

Question 9

how do you find a HA when the degree of numerator = degree of denominator

Answer 9

y=leading coefficient top/leading coefficient bottom

Question 10

how do you find a HA when the degree of numerator < degree of denominator

Answer 10

y=0

Question 11

how do you find OA when the degree of numerator >degree of denominator

Answer 11

y=quotient of long division

Question 12

how do you find a VA

Answer 12

bottom=0 after you factor and cancel

Question 13

how do you find the hole

Answer 13

factors that cancel when simplifying =0

Question 14

how do you find the x-intercept

Answer 14

top=0 after factor and cancel

Question 15

how do you find the y-intercept

Answer 15

set x=0

Question 16

how do you find the domain

Answer 16

everything except denominator=0

Question 17

how do you find the range

Answer 17

calculator

Question 18

how do you know if there is a hole on a table

Answer 18

x=number y=undefined or the y-values stay around the same number
ex.| -2 | undefined |

Question 19

how do you know if there is a VA on a table

Answer 19

as x approaches the VA, y increases rapidly
ex. |2.1|94|
|2.01|904|
|2.001|9004|
VA at 2

Question 20

how do you know if there is a HA on a table

Answer 20

as y approaches the HA, x increases rapidly
ex. |-1|1|
|-10|-0.125|
|-100|-0.0102|
|-1000|-0.001|
HA at 0

Question 21

how do you solve a word problem like:
Emma can clean a large tank at an aquarium in about 6 hours. When Emma and Ella work together, they can clean the tank in about 3.5 hours. How long would it take Ella to clean the tank by herself?

Answer 21

1/Individual timehours together + 1/other individual timehours together=1
ex. (1/6)3.5 + (1/x)3.5 =1

Question 22

how do you solve a distance|speed|time word problem?
ex. When it was raining, Zander drove for 120 miles. When the rain stopped, he drove 300 miles and 20mph faster than he did when it was raining. If Zander drove for a total of 10 hours, how fast did he drive when it was raining?

Answer 22

create a 3x2 table for distance, speed, time, and other variables
create an equation based on the given information
solve
ex. 120/x + 300/x+20 = 10
answer: 30mph, -8 extraneous