Identifying Domain (Set builder notation!)
The number of concert tickets sold. Let x = the number of tickets.
{x | x ∈ ℤ, x ≥ 0}
x: 0, 1, 2, 3 · f(x): 5, 8, 11, 14
f(x) = 3x + 5
f(x) = 7 · 2ˣ, {x | x ∈ ℝ, x ≥ 0}
Exponential (GF 2),Continuous
√50
5√2
x⁴ · x⁵
x⁹
The distance a car has traveled x hours after it starts driving.
{x | x ∈ ℝ, x ≥ 0}
x: 0, 1, 2, 3 · f(x): 2, 6, 18, 54
f(x) = 2 · 3ˣ
x: 1, 2, 3, 4 · f(x): 3, 7, 11, 15
Domain: {x | x ∈ ℕ}
Linear (ROC 4), Discrete
√72
6√2
(x³)⁴
x¹²
The cost of an online order of x pizzas. Every order has at least 1 pizza.
{x | x ∈ ℕ}
A gym costs $40 to join plus $15 per month. Let x = months.
f(x) = 15x + 40
The total cost of x movie tickets at $12 each.
Linear, discrete
∛54
3∛2
2x⁻³
2/x³
A plant’s height is measured once at the end of each week. Let x = the number of weeks.
{x | x ∈ ℤ, x ≥ 0} (measured only once a week, so discrete)
x: 1, 2, 3, 4 · f(x): 7, 11, 15, 19
f(x) = 4x + 3
x: 1, 2, 3, 4 · f(x): 1, 4, 9, 16, {x | x ∈ ℕ}
Neither (differences 3, 5, 7; ratios not constant), discrete
√(x⁷)
x³√x
(20x³) / (5x⁷)
4/x⁴
Write your own situation with the domain {x | x ∈ ℝ, x ≥ 0}.
It must be measured at every moment, starting at 0 (for example, water in a tank x minutes after it starts filling).
A town of 2,000 people grows by 10% each year. Let x = years.
f(x) = 2000(1.1)ˣ
A camera records the area of a bacteria colony at every moment. The area doubles every day.
Exponential, continuous
√(25x⁵)
5x²√(x)
(3x²)³ / (9x⁴)
3x²