Restrictions and Domain
What is the restriction of 2x/3x - 6? How do you know?
x ≠ 2 , 3(2) = 6, 6 - 6 = 0 and we cannot divide by 0.
What are the four steps to multiplying rationals?
1) If necessary, factor the numerator and denominator of each rational expression.
2) If possible, "cancel" common factors.
3) Multiply the numerator.
4) Multiply the denominator.
What three-word phrase do we use to divide rationals? What does it mean?
Keep, change, flip! It means we should keep the first fraction, change the division sign to multiplication, and then flip the second fraction.
Find the LCD of 1/x2 - 16 and 1/(x - 5)
(x - 4)(x + 4)(x - 5)
What is the definition of a proportion? Give an example.
ex) x - 3/x = x - 5/x
Write the definition of domain and write the general template of it.
The domain is the set of all values that x can be.
General template: (-∞, ____) ∪ (____, ∞)
Multiply 1/3 · 6/4
1/2
Divide 8/10 ÷ 2/5 Put your answer in simplest form.
2
Add 3x2 + 9x + 2/5x + 2x2 - 5x - 6/5x
5x2 + 4x - 4/5x
Solve x - 3/x + 1 = 2x - 5/x + 1
2
Fill in the blanks:
When finding the domain of a rational function, we:
1) Find the ________________.
2) Write possible x-values using ___________ ________________.
When finding the domain of a rational function, we:
1) Find the restrictions.
2) Write possible x-values using interval notation.
Multiply (x + 3)(x + 2)/(x + 3)(x - 2) · (x - 5)(x + 5)/(x - 1)(x - 5)
(x + 2)(x + 5)/(x - 2)(x - 1)
Divide (x + 1)(x - 1)/(x + 2)(x - 2) ÷ (x - 1)(x + 1)/(x - 2)(x + 2) Put your answer in simplest form.
1
Subtract 3x2 + 9x + 2/5x - 2x2 - 5x - 6/5x
x2 + 14x + 8/5x
Solve 15/x - 5 = 5
x ≠ 5, x = 8
How many restrictions does 10x/x2 - 64 have?
What are they?
There are two restrictions: x ≠ -8, 8
Multiply (x + 8)(x - 8)/(x + 3)(x + 2) · x2 - 9/x2 - 12x + 32
(x + 8)(x - 3)/(x + 2)(x - 4)
Divide (x - 4)(x - 4)/x2 - 2x - 8 ÷ 1/(x - 5)
(x - 4)(x - 5)/(x + 2)
Add 8/x2 - 6x - 16 + 9/x2 - 3x - 40
17x + 58/(x + 5)(x - 8)(x + 2)
Give an example of how solving proportions can help us in real-life. Be as specific as possible.
Baking, traveling, currency conversions, and so much more!
Find the domain of the following function: f(x) = x - 4/x2 - x - 30
(-∞, -5) ∪ (-5, 6) ∪ (6, ∞)
Multiply x2 + 5x - 36/x2 + 5x + 6 · x2 - 4/x2 + 4x - 45
(x - 4)(x - 2)/(x + 3)(x - 5)
Divide x2 - 2x - 15/8x + 20 ÷ 2/4x + 10
(x - 5)(x + 3)/4
Subtract 2x + 1/x - 5 - 4/x2 - 3x - 10
2x2 + 5x - 2/(x + 2)(x - 5)
In Japan, 1 Yen is equivalent to 0.0075 US dollars. If Marty goes to Japan and brings $20, does he have enough to buy sushi that costs 3000 Yen?
How do you know? Please show your work.
No, Marty would have enough to buy sushi that is worth 2,666.67 Yen, but not more.