Relations and Fuctions
When is a relation a function?
When each independent variable has exactly one output.
Model the following rule with a table of values and a graph:
f(x) = (-1/2)x - 3
(-2, -2), (-1, -2.5), (0, -3), (1, -3.5), (2, -4)
Graph
What is the difference between a linear equation and a direct variation?
A direct variation must go through the origin, and a linear equation does not.
Suppose y varies inversely with x. Write the equation for the inverse variation:
x = 88, when y = 0.05
y = 4.4 / x
There is a common difference between each term.
Are the following coordinates a function or just a relation:
(11, -2), (12, -1), (13, -2), (20,7)
It is a function
Write the function rule for the following values:
x , f(x)
2 , 3
4 , 5
6 , 7
8 , 9
f(x) = x + 1
What is the difference between continuous data and discrete data?
Continuous data includes all values between the values we graph, and discrete data does not.
The following pair of points are on a graph of an inverse variation. Find the missing value:
(9 , x) & (3 , 12)
x = 4
Find the common difference and what are the next three terms:
14, 21, 28, ...
+7; 35, 42, 49
Are the following coordinates a function or just a relation:
(-2, -1), (-1, 0), (6, 3), (-2, 1)
It is a relation
Write the function rule for the following values:
x , f(x)
0 , 0
3 , 6
6 , 12
9 , 18
f(x) = 2x
Is the following a direct variation:
y = 2x + 5
No, the +5 does not make it a direct variation.
The following pair of points are on a graph of an inverse variation. Find the missing value:
(4 , 2.65) & (y , 4.24)
y = 2.5
What is the formula for an arithmetic sequence?
A(n) = a (n - 1)d
How can you determine if a graph is a function or a relation?
By using the vertical line test.
Write the function rule for the following values:
x , f(x)
-2 , -1
-1 , -2
0 , -3
1 , -2
2 , -1
f(x) = |x| - 3
Write the equation of the direct variation that includes the given point:
(-2, 6)
y = -3x
Find the constant of variation when:
y = 10 and x = 7
k = 70
What is the 100th term in the sequence:
9, 13, 17, ...
405
Find the range of the following function when the domain is {-4, 0, 1, 5}.
Function: p = q^2 +1
{17, 1, 2, 26}
Write a function rule for the following situation:
the distance you run in feet D(m) when you know the distance in miles m
D(m) = 5280m
Is the following data a direct or inverse variation, and what is the equation for the data:
x , y
3 , 24.6
5 , 41
10 , 82
direct variation: y = 8.2x
Is the following data a direct or inverse variation, and what is the equation for the data:
x , y
0.4 , 28
1.2 , 84
0.9 , 63
direct variation: y = 70x
9, 6, 3, ...
-288