NAME _____________________________________________ DATE ____________________________ PERIOD _____________
1-1 Practice
Functions
Write each set of numbers in set–builder and interval notation, if possible.
1. {–3, –2, –1, 0, 1, …}
2. – 6.5 < x ≤ 3
3. all multiples of 2
4. x < 0 or x > 8
Determine whether each relation represents y as a function of x.
5. The input value x is a car’s license plate number, and the output value y is the car’s make and model.
6.
7.
8. –x + y = 3x
9. x = 5(𝑦 − 1)2
Find each function value.
10. h(x) = 𝑥 2 – 8x + 1
11. f(a) = –3√𝑎2 + 9
a. h(–1)
a. f(4)
b. h(2x)
b. f(3a)
c. h(x + 8)
c. f(a + 1)
State the domain of each function.
12. g(x) = √− 3𝑥 − 2
2𝑡 − 6
13. h(t) = 𝑡 2 + 6𝑡 + 9
NAME _____________________________________________ DATE ____________________________ PERIOD _____________
Find each function value.
3𝑥 2 + 16 if 𝑥 < −2
14. Find f(–4) and f(11) for the piecewise function f(x) = {√𝑥 − 2 if − 2 < 𝑥 ≤ 11.
−75 if 𝑥 > 11
𝑥 + 45 if 𝑥 ≤ −1
15. If g(x) = {
, find g(–5) and g(36).
81 − 𝑥 if 𝑥 > −1
√2𝑥 if 𝑥 < 3
16. If f(x) = {2𝑥 + 10 if 3 ≤ 𝑥 < 8, find f(3) and f(8.5).
42 if 𝑥 ≥ 8
17. DEER A park’s deer population over five years can be modeled by f(d) = –3𝑑4 + 43𝑑3 – 185𝑑2 + 350d – 59. Estimate
f(3) and f(5), the populations in the third and fifth years.
18. TIPPING A restaurant patron has decided to leave a 15% tip for meals costing up to $40, an 18% tip for meals
costing at least $40 but less than $100, and a 20% tip for meals costing $100 or more. Write a piecewise function to
describe the total amount t the patron will pay in terms of the meal cost c.
19. ELEVATOR An elevator starts with 12 people on a building’s eighth floor. One person exits to each floor. The
lowest level is two floors below ground level. The function f(ℓ) = ℓ + 4 gives the number of people on the elevator after
a person exits to that level.
a. Write the relevant domain in set-builder notation.
b. Write the range in set-builder notation.