Relations to Functions
Function Rules, Tables, Graphs
Writing a Function Rule
Direct Variation
Inverse Variation
100
Define relation.
A relation is a set of ordered pairs. These ordered pairs can represent quantities such as age and height.
100
This is what makes a function different from other mathematical equations.
What does "every x has one unique y" describe?
100
The f(x) values for x = 1,2,3,4 satisfy this function which is in this function family. x f(x) 1 -1 2 0 3 1 4 2
What is f(x) for the linear function "f(x) = x -2" when x = 1,2,3,4?
100
What kind of situation does direct variation describe?
When one set of data increases, the other set of data increases. When one set of data decreases, the other set of data decreases.
100
What type of situation does in inverse variation describe?
When one set of data is increasing, the other set is decreasing.
200
Define function.
A function is a relation that assigns exactly one output (range) value for each input (domain) value.
200
Describe function notation
A function is in function notation when you use f(x) to indicate outputs. You read f(x) as "f of x" or "f is a function of x". The notations g(x) and h(x) also indicate functions of x. It is a way to represent a function algebraically or a way to name a function.
200
The volume "v(s)" of a cube when you know the length of a side "s". v(s) = _____
What is v(s)=s^3?
200
Is this a direct variation? If it is, find the constant of variation.
-x = 10y
yes y = 5x
200
Suppose y varies inversely with x. Write an equation for:
x = 6 when y = 1
xy = 6
300
What methods can be used to determine if a set of ordered pairs or an equation is a function?
mapping, vertical line test,identifying if any x-values repeat
300
These are four ways you can represent a function.
What are tables of values, graphs, mapping diagram,ordered pairs, or equations.
300
The function d(n) represents miles traveled after n hours at a constant speed of 45 miles per hour. d(n)=______
What does this function represent? d(n) = 45n
300
Write an equation of the direct variation that includes the given point.
(-8,10)
y = -5/4x
300
The pair of points represents in inverse variation. Find the missing value.
(r, 100) and (75,25)
r = 18.75
400
Use mapping to determine whether the relation is a function: [(3,7), (3,8), (3, -2), (3,4), (3, 1)]
no
400
A function family that looks like the letter u is called what?
Quadratic Function
400
Beginning at 54, for every increase in r of 1, t(r) decreases by 50%. t(r) = _____
How could you describe the pattern of this function in words? t(r)=54(.5)^r
400
Define the variables. Then write a direct variation to model the relationship.
The perimeter p of a regular octagon varies directly with the length l of one side of the octagon.
P(l) = 8l
400
Does the data in the table represent a direct variation or an inverse variation? Write an equation to model it.
x y
3 24.6
5 41
10 82
direct; y = 8.2x
500
Is this a function? Why or why not?
No, there are 2 arrow coming off of the number 2. So 2 has an output of 20 and 40.
500
This equation represents this type of function family:
f(x) = 2x + 3
What is a linear function?
500
At the beginning of last month, your stock portfolio was worth $2653, but it decreased by 10% each day. This is the function that describes that situation and the amount of money you have left.
Describe the pattern of this function (money remaining in terms of days since beginning of last month) in words: m(d)=2653(.9)^d m(30)=112.46
500
The price of a turkey depends on its weight. Suppose turkeys sell for $0.59 per lb. Write a rule to describe the function. What is the price of a 14lb turkey? If you had $10 to buy a turkey, how big a turkey could you buy?
P(t) = 0.59t
$8.26
about 16.9lb
500
How does direct variation and inverse variation differ?
graphs: direct thru point of origin; direct positve, inverse negative
constant: direct : ratio inverse: product