Number Sets
What is the difference between a rational and a irrational number?
Rational can be expressed as a ratio of two integers while irrational cannot be expressed that way as their decimals cannot terminate or repeat but rational can
What is the square root of 49?
7
Expand out (4y)3
(4y)(4y)(4y)
What is the difference between domain and range?
The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes.
Transform Point (-1,3) 4 units right
(3,3)
Classify each number by category: real, rational, integer, whole, natural and irrational. Remember some numbers can be classified more than once:
.5129,43,0,-5/2, square root of two
.5129: Real and Rational
43: All except irrational
-5/2: Real and rational
Square root of two: irrational
Without a calculator, estimate to the nearest tenth of the square root of 73
8.5
-(3/4)-4
-256/81
For the function f(x)=7x-4 evaluate f(0),f(3/2), f(-12)
-4,13/2,-88
What happens when the y-axis reflects, what happens when the x-axis reflects
X-coordinates change, y- coordinates change
Use interval notation to represent the set of the numbers:
-10<x<=10,x>30,x does not equal 5.
(-10,10],(30, inf), (-inf,5) and (5, inf)
Simplify the equation:
2*sqrt(2)/sqrt(3)
2*sqrt(6)/3
Convert the speed of light from kilometers/second to meters/minute. Remember speed of light is 3*105 km/s
1.8^10 m/min or 180*108 m/min
Explain why -5<x<5 is not a reasonable domain for 1/(x-3)
When x=3 the graph is undefined
What happens when the table is translated two units down?
The entire graph shifts two units down.
Are all square roots irrational? Why or why not?
They are not always irrational because perfect squares exist.
Given that sqrt(2+2)=2 does that mean sqrt(a+a)=a. Explain why or why not.
It doesn't.
Simplify the given expression: (-4)-2
1/16
Write a function: Leona's salary is 250 plus 5% of what her sales are for the week
250+.05x=f(x)
What is the difference between stretching and compression?
Stretching is when you pull points away from the y- axis, compression pulling points towards it.
Describe the set {-9,-7,-5,-3,-1}
The range is -9 to -1 and they're all odd.
The original design for the city of Savannah, GA was based on a grid-like system of wards. At one time the city included a total of 24 wards. Each ward was square and together it covered 8,640,000 sq. ft. Find the appropriate dimensions of a ward.
600 by 600 ft
Use the quotient of powers property to show why 00 is undefined
00=01-1=0/0 which is undefined
Identify the independent and dependent variable for the situation and the create a reasonable domain.
As long as a minimum of 15 shirts are ordered, the cost for an order of T-shirts is $4.25 per shirt.
independent: # of shirts
dependent: total cost
domain: x>=15
Suppose two transformations are performed on a single point: a translation and a reflection. Does the order matter and create a difference as well as the type of translation or reflection?
Order is important with horizontal translation and reflection of the y-axis; vertical translation and reflection of the x-axis. However its not important the other way around.