Algebra 2 Notes
2-1 Relations and Functions
Recall
Domain: all x values
Date:
Range: all y values
VOCABULARY
Function: domain does not repeat; graph passes the vertical line test.
One-to-one Function: range does not repeat
Onto function: each element of the domain corresponds to an element of the domain (no y left over)
Discrete relation: domain is a set of individual points
Continuous relation: domain has an infinite number of elements and can be graphed with a line or smooth
curve
Independent variable: values that make up the domain, input (often x)
Dependent variable: values that make up the range because it depends on x, output (often y)
Function notation: equations that represent functions are written in this notation
y = 2x + 3 can be written as f(x) = 2x + 3 ***** f(x) is y!
Vertical Line Test:
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Examples:
State the domain and range of the relation. Does the relation represent a function, if so is it one-to-one,
onto, both or neither?
1)
2)
x y
x y
-1
0
1
2
3
-5
-3
-1
1
3
2
4
6
2
5
10
12
14
0
3
State the domain and range of each relation. Then determine whether each relation is a function. If it is a
function, determine if it is one-to-one, onto or both.
3) { (0.5,3), (0.4, 2), (3.1, 1), (.4, 0) }
5)
4) { (-5,2), (4,- 2), (3,-11), (-7, 2) }
6)
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Graph a relation
For each of the following, make a table of values, graph the equation and determine the domain and
range. Then determine whether the equation is a function, is on-to-one, onto, both, or neither.
1
𝑦 = 𝑥2 + 1
𝑦 = 2𝑥 − 3
Evaluate a Function – using function notation
Given 𝑓(𝑥) = 2𝑥 2 − 8, find each value
a) 𝑓(6)
b) 𝑓(2𝑦)
Try this! Given 𝑓(𝑥) = 𝑥 3 − 5, find each value.
11) 𝑓(−2)
12) 𝑓(2𝑎)
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