Properties
Describe the difference between the associative and commutative properties of addition.
Associative means you can group the numbers in any order with parentheses and commutative means you can change the order you add numbers but the answer stays the same.
If f(x) = -2x - 3 and g(x) = x^2 + 5x, find g(2).
14
Define domain and range. How do we write these?
Domain: possible x-values
Range: possible y-values
We write these as sets (with { }) or as inequalities when there are infinitely many numbers.
Ms. Hernandez boarded her dog at a kennel for 4 days. It cost $28.90 per day, and she had a coupon for $5 off. What was the final cost for boarding her dog?
$110.60
Jocelyn makes x dollars per hour working at the grocery store and n dollars per hour babysitting. Write an expression that describes her earnings if she babysat for 25 hours and worked at the grocery store for 15 hours.
25n + 15x
Give an example of two numbers that are multiplicative inverses where one of the numbers is a negative integer.
If f(x) = -2x - 3 and g(x) = x^2 + 5x, find f(0) - 7.
-10
What test should you use to determine if a graph is a function?
Vertical Line Test
Is $12 enough to buy a half gallon of milk for $2.49, a bag of apples for $4.35, and four cups of yogurt that cost $0.89 each? Explain.
Yes because it costs about $10.50.
If 4 is added to twice a number, the result is 10 less than the number. Write an equation to solve for the number but don't solve.
4 + 2n = n - 10
Which property is shown: If w = 5, then 2w - 8 = 2(5) - 8 = 2.
Substitution Property
If f(x) = -2x - 3 and g(x) = x^2 + 5x, find f(4y).
-8y - 3
Write a mapping of the following relation: {(4,-3), (1,3), (7,-2), (2,-2), (1,5)}.
Draw on board.
Jose has a board that is 44 inches long. He wishes to cut it into two pieces so that one piece will be will be 6 inches longer than the other. How long should the shorter piece be?
p + 6 + p = 44
p = 19 inches
The sum of four consecutive integers is -18. What is the greatest of these integers? Write an equation but do not solve.
x + (x + 1) + (x + 2) + (x + 3) = -18
or 4x + 6 = -18
Which property is shown: -39(1) = -39?
Multiplicative Identity
If f(x) = -2x - 3 and g(x) = x^2 + 5x, find 3g(n).
3n^2 + 15n
Sketch an example of a graph that is not a function.
Answers vary.
Paula received a paycheck of $585. This amount reflects her weekly earnings less 10% of her earnings for deductions. How much was she paid before deductions were taken out?
585 = t - 0.10t
t = $650
Ally sold 18 boxes of girl scout cookies. This was 20% of the number of boxes that Kayla sold. How many boxes did Kayla sell? (Use the percent proportion.)
18/k = 20/100
k = 90
Find the value for x and then name the property used: 7 * 2 = 7 * x.
x = 2; Reflexive Property
If f(x) = -2x - 3 and g(x) = x^2 + 5x, find f(c - 5).
-2c + 7
Graph the equation y = -4x -1. Make a table of four ordered pairs. Is this a function? What is the domain and range?
Graph: sketch on board. Ordered Pairs (answers vary): (0,-1) (1,-5) (2,-9) (3,-13)
Yes it is a function.
Domain and Range: all real numbers
The family bowling alley charges $4 per game and $1 for shoe rental. The big bowling alley charges $3.75 per game and $2 for shoe rental. How many games would ONE person need to play for the cost at the bowling alleys to be equal?
4g + 1 = 3.75g + 2
g = 4 games
You buy eight goldfish for x dollars per goldfish. You buy 2 rainbow fish which cost 6 dollars more than each goldfish. You spend a total of $37. Write an equation that would solve for x but don't solve.
8x + 2(x + 6) = 37