A relation is a set of ordered pairs. These ordered pairs can represent quantities such as age and height.
100
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.
100
Write a function rule for this table:
x y
1 -1
2 0
3 1
4 2
f(x) = x -2
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
What are the three ways you can model functions?
tables, graphs, equation rules
200
Write a function rule:
x y
1 3
2 6
3 9
4 12
y = 3x
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 an equation is a function?
mapping, vertical line test
300
Define continuous data and discrete data. How do you graph them?
Continuous data occur when there are numbers between any two sets of data values. Discrete data are data that involve a count of items. Use a solid line to graph continuous data and a point to graph discrete data.
300
Write a function rule:
the total distance d(n) traveled after n hours at a constant speed of 45 miles per hour
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
What will the graph look like for the following function rules?
y = [x] + 2
f(x) = -x^2 - 1
f(x) = 2x +7
V
parabola
linear
400
At a supermarket salad bar, the price of a salad depends on its weight. Salad costs $0.19 per ounce. Write a rule to describe the function. How much would an 8 oz salad cost?
f(x) = 0.19x
$1.52
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
Use the vertical line test for examples 32, 33, 34, and 35 to see if the graphs represent functions.
32: yes 33: no 34: NO 35: YES
500
The function A(l) = 1/2 t^2describes the area of an isosceles right triangle with leg l. Make a table of values for l = 1,2,3, and 4.
l A(l)
1 0.5
2 2
3 4.5
4 8
500
Write a function for:
the volume V(n) of a cube when you know the length (n)of a side.
V(n) = n^3
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