Functions
What makes a relation a function?
Each input has only one output.
What’s the rule for y if each x is multiplied by 4?
y = 4x
What type of sequence adds the same number each time?
Arithmetic sequence
In y = 3x, which variable is independent?
x
Solve: x + 5 = 9
x=4
Is this a function? (2,5), (3,6), (2,7)
❌ No, because input 2 has two outputs (5 and 7).
Write a rule for this table: (x: 1, 2, 3) → (y: 5, 7, 9)
y = 2x + 3
Find the next term: 4, 7, 10, 13, ___
16
The number of hours you work and the money you earn. Which is dependent?
Money earned depends on hours worked.
Solve: 3x -3 = 12
5
On a graph, how can you tell if it’s a function?
Use the vertical line test — if a line touches the graph twice, it’s not a function.
If y = 3x – 8, what’s the value of y when x = 6?
y = 3(6) – 8 = 10
What’s the common difference in 5, 9, 13, 17?
+4 (add 4)
In an experiment, you change the temperature and measure plant growth. Which is the independent variable?
Temperature
Solve: 2x – 7 = 9
x=8
If f(x) = 2x + 3, what is f(4)?
f(4) = 2(4) + 3 = 11
A taxi ride costs $3 plus $2 per mile. Write the rule.
y = 2x + 3
Write a rule for the sequence: 3, 6, 9, 12, …
Add by 3
If y = 4x + 1, what happens to y when x doubles?
y also doubles plus 1 more.
Solve: 4(x – 2) = 12
x=5
What's the domain and range?
x y
2 6
3 8
4 10
5 8
7 5
Domain: 2,3,4,5,7
Range: 5,6,8,10
number of cases of bottled water, c number of bottles of water, b
1 24
2 48
5 120
10 240
20 480
b= 24c
If the 1st term is 2 and the common difference is 5, find the 10th term.
47
Explain how to find which variable is dependent.
The dependent variable changes because of the independent one. (It’s the “result.”)
Solve: 5x + 3 = 2x + 18
x=5