Restrictions
What is the definition of a restriction?
A restriction is what x cannot equal. It would give us a zero in the denominator.
What is the definition of domain?
The domain is the set of all values that x can be.
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?
Keep, change, flip!
What is the definition of a proportion?
A proportion says that two ratios (or fractions) are equal.
What is the restriction of 2x/3x
How do you know?
x ≠ 0
3(0) = 0
We cannot divide by 0.
(-∞, ______) ∪ (______, ∞)
Multiply 1/3 x 6/4
Put your answer in simplest form.
6/12 --> 1/2
Divide 8/10 ÷ 2/5
Put your answer in simplest form.
2
Solve x - 3/x + 1 = 2x - 5/x + 1
2
Nora says that x2 - 2x - 5 / 100 does not have any restrictions. Is she correct? Why or why not?
Nora is correct! The denominator for x2 - 2x - 5 / 100 will always be 100 since there are no variables in the denominator. There are no x values that can make the denominator 0.
What are the two steps in finding the domain of a rational function?
1) Find the restriction(s)
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 + 2) ÷ (x + 1)/(x + 2)
Put your answer in simplest form.
1
Solve 15/x - 5 = 5
8
What are the 4 steps to finding the restriction(s) of a rational?
1) If necessary, factor the denominator.
2) Set each factor in the denominator equal to zero.
3) Solve for the x.
4) Write the restriction(s)
Find the domain of the following rational function:
f(x) = 10x - 14/ x + 3
(-∞, -3) ∪ (-3, ∞)
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)/x2 - 2x - 8 ÷ 1/(x - 5)
(x - 5)/(x + 2)
Give an example of how solving proportions can help us in real-life.
Baking, traveling, currency conversions, and so much more!
State the restrictions of x - 5/x2 - 16
x ≠ -4, 4
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
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, he would have enough to buy sushi that is worth 2,666.67 Yen, but not more.