Functions
Define function.
Describes the relationship between domain and range. Each input has ONE output.
3 < -5x + 2x
x < -1
-20 = -4x-6x
2
y = -5
5x + 4y = -20
(0,5)
A man has two more nickels than dimes, and has $1.15 in total. How many coins of each kind does he have?
9, 7
Find four consecutive even integers such that 2 times the sum of the first and second is 14 more than 3 times the fourth.
28, 30, 32, 34
Define domain. Define range.
Domain - independent, input, x-values
Range - dependent, output, y-values
-x - 4x > -10
x < 2
7x/4+5x/3=0
x = 0
y = x - 3
y = 4x - 9
(2,-1)
The sum of three consecutive odd numbers is 93. Find the numbers.
29, 31, 33
FOIL.
(2a−1)(8a−5)
16a2 −18a+5
Given the function and a domain, find the range.
f(x) = −6x − 1; D={-2, -1, 0, 5}
R = {11, 5, -1, -31}
-3 - 6(4x+6) > -111
x < 3
-3(4x+3) + 4(6x+1) = 43
4
4x +2y = 10
x - y = 13
(6,-7)
DOUBLE JEOPARDY!!
Working together, Mary and Trevon can inflate twenty balloons in 7.34 minutes. Had he done it alone it would have taken Trevon 14.1 minutes. How long would it take Mary to do it alone?
15 minutes 18 secs 36 millisecond
(7x−6)(5x+6)
35x2 +12x−36
h(t)= |t + 2| + 3; Find h(6)
11
6 - 4(6x+7) ≥ 122
x ≤ -6
2x + 10 = 13/3
x = 9/2 or 4.5
8x - 6y = -20
-16x + 7y = 30
(-1,2)
Mrs. Robinson cashed a check for $500 in five and ten dollar bills. The teller gave her 60 bills. How many five-dollar bills did she receive?
20 five-dollar bills
Factor
6x2 + 5x − 6
(2x + 3)(3x − 2)
f(x) = x2 − 3x; Find f(−8)
88
28 - x ≥ 7(x - 4)
x ≤ 7
|-4 + 5x| = 16
x = 4; x =-12/5
-24 - 8x = 12y
1 + 5y/9 = -7x/18
(6,-6)
Mandy decides to promote the new product she is selling by offering a $100 discount for customers ordering 12 or more units of the new product. If Neil orders 12 units and receives a bill for $620, what is the price of each unit?
$60
Factor
6x2 +7x−49
(3x − 7)(2x + 7)
h(t) = −2⋅5−t−1; Find h(−2)
-10
-6(1 + 7x) + 7(1 + 6x) ≤ -2
No solution.
3 |−8x| + 8 = 80
x = -3; x = 3
-16y = 22 +6x
-11y - 4x = 15
(-1,-1)
Working together, Kim and Jennifer can install a new deck in 6.28 hours. Had she done it alone it would have taken Jennifer 13.7 hours. How long would it take Kim to do it alone?
11 hours 36 minutes
A safe contains 120 coins, the value of which is $10. If the coins consist of nickels and dimes, how many of each kind are in it?
40,80
h(x) = 4x − 2; Find h(x+2)
4x + 6
DOUBLE JEOPARDY!!
-2(5 + 6x) < 6(8 - 2x)
24x - 22 = -4(1-6x)
No solution.
-16 + 20x - 8y = 0
36 = -18y - 22x
(0, -2)
The local store is running a special on bacon and eggs. If one of your neighbors paid $30 for 10 kg of bacon and 3 dozen eggs, and another neighbor paid $48 for 20 kg of bacon and 2 dozen eggs, what should you pay for 7 kg of bacon and 4 dozen eggs?
$26.70
DOUBLE JEOPARDY!!
FOIL
(4p−1)2
16p2 −8p+1